A. 149 kg baseball moving at 17. 7 m/s is caught by a 57 kg catcher at rest on an ice skating rink,


wearing frictionless skates. With what speed does the catcher slide on the ice?


Do NOT put in units or it will be marked wrong! The answer's value only! Please round each


answer to 3 places.


Mava + MbVb = (Ma+b)(Va+b)

Two advantages of alkaline accumulators over lead-acid accumulators are:

1. Higher energy density: Alkaline accumulators have a higher energy density than lead-acid accumulators, which means they can store more energy in the same volume or weight of battery. This makes them ideal for portable devices where size and weight are important factors.

2. Longer cycle life: Alkaline accumulators have a longer cycle life than lead-acid accumulators, which means they can be charged and discharged many more times before they need to be replaced.

This makes them a more cost-effective and reliable option for applications where the battery will be used frequently, such as in electric vehicles or renewable energy systems.

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The volume of the terrarium is approximately 4.69 cubic feet.  

The volume of the terrarium, we can use the formula for the volume of a rectangular prism:

V = lwh

We know that the length of the terrarium is 20 inches, the width is 15 inches, and the height is 12 inches. Therefore, we can substitute these values into the formula:

V = 20 inches * 15 inches * 12 inches

V = 300 inches

We want the volume in cubic inches, so we can convert cubic inches to cubic feet by dividing by 63:

V = 300 inches / 63

V = 4.69 cubic feet

Therefore, the volume of the terrarium is approximately 4.69 cubic feet.  

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Answer:To solve this problem, we need to use the equations of motion and kinematics.

1. What is the position of the car after 4 seconds?

The position of the car after 4 seconds can be found using the equation:

position = initial position + (initial velocity x time) + (1/2 x acceleration x time^2)

Plugging in the values, we get:

position = 0 + (21 x 4) + (1/2 x 0 x 4^2) = 84 meters

Therefore, the position of the car after 4 seconds is 84 meters.

2. What is the position of the truck after 4 seconds?

The position of the truck after 4 seconds can be found using the equation of motion for uniform acceleration:

position = initial position + (initial velocity x time) + (1/2 x acceleration x time^2)

Initial velocity of the truck is zero, and the acceleration is 1.2 m/s^2. The initial position of the truck is 310 meters ahead of the car.

Plugging in the values, we get:

position = 310 + (0 x 4) + (1/2 x 1.2 x 4^2) = 326.4 meters

Therefore, the position of the truck after 4 seconds is 326.4 meters.

3. What is the velocity of the truck upon impact with the car?

To find the velocity of the truck upon impact with the car, we need to use the equation:

final velocity = initial velocity + acceleration x time

The initial velocity of the truck is zero, the acceleration is 1.2 m/s^2, and the time is the time it takes for the collision to happen.

4. How much time passes before the collision happens?

To find the time it takes for the collision to happen, we need to use the equations of motion and kinematics.

The position of the car at the time of the collision is the same as the position of the truck at the time of the collision. Let's call this position "x".

Using the equation of motion for the car, we have:

x = 0 + (21 x t) + (1/2 x 0 x t^2) = 21t

Using the equation of motion for the truck, we have:

x = 310 + (0 x t) + (1/2 x 1.2 x t^2) = 0.6t^2 + 310

Setting these two equations equal to each other, we get:

21t = 0.6t^2 + 310

Simplifying and solving for t, we get:

t = 23.98 seconds

Therefore, the time it takes for the collision to happen is approximately 24 seconds.

5. Where do the car and truck collide?

The position of the collision can be found by plugging the time into either the equation of motion for the car or the equation of motion for the truck.

Using the equation of motion for the car:

position = 21 x 23.98 = 503.58 meters

Using the equation of motion for the truck:

position = 0.6 x (23.98)^2 + 310 = 503.58 meters

Therefore, the car and truck collide at a position of 503.58 meters.

Explanation:

The force of attraction between the two masses is [tex]3.335 \times 10^{-8} N[/tex].

The force of attraction between two masses is given by the gravitational force equation, which is expressed as:

[tex]$F = G \cdot \frac{m_1 \cdot m_2}{r^2}$[/tex]

where F is the force of attraction, G is the gravitational constant ([tex]$6.67 \times 10^{-11} , \text{N}\cdot\text{m}^2/\text{kg}^2$[/tex]), [tex]m_1[/tex]1 and [tex]m_2[/tex] are the masses of the two objects, and r is the distance between the centers of the two masses.

In this case, [tex]m_1[/tex] = 100 kg, [tex]m_2[/tex] = 50 kg, and r = 100 m. Substituting these values into the equation, we get:

[tex]$F = 6.67 \times 10^{-11} , \text{N}\cdot\text{m}^2/\text{kg}^2 \cdot \frac{(100 , \text{kg}) \cdot (50 , \text{kg})}{(100 , \text{m})^2}$[/tex]

[tex]F = 3.335 \times 10^{-8} N[/tex]

It is worth noting that the force of attraction between the two masses is very small, which is due to the large distance between them. The gravitational force decreases rapidly with distance, so as the distance between the two masses increases, the force of attraction decreases as well.

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Between point A and point B, the net work done on the object is: +20 joules, indicating that the system has gained energy overall, likely in the form of kinetic or potential energy.

As the object moves from point A to point B, it experiences both conservative and nonconservative forces. Conservative forces, such as gravity and spring forces, have the ability to store energy in the form of potential energy, and the work done by these forces can be recovered. Nonconservative forces, like friction or air resistance, dissipate energy as heat, and the work done by these forces cannot be recovered.

In this specific case, the nonconservative force does -30 joules of work, which implies that energy is being removed from the system as heat. On the other hand, the conservative force does +50 joules of work, meaning energy is being stored as potential energy in the system.

To find the net work done on the object as it moves from point A to point B, you can simply add the work done by both forces. In this case, the net work is -30 joules (nonconservative force) + 50 joules (conservative force) = +20 joules.

So, between point A and point B, the net work done on the object is +20 joules, indicating that the system has gained energy overall, likely in the form of kinetic or potential energy.

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Microwaves can be used to cook food. If a microwave oven uses waves that are 1 cm (0. 01 m) long then 3.00 x [tex]10^{10}[/tex] Hz is the frequency of these waves.

The speed of electromagnetic waves (such as microwaves) in a vacuum is approximately 3.00 x [tex]10^{8}[/tex] m/s.

The frequency of a wave is given by the formula

f = c / λ

Where f is the frequency, c is the speed of light, and λ is the wavelength.

In this case, the wavelength is 0.01 m, so we can calculate the frequency as

f = 3.00 x [tex]10^{8}[/tex] / 0.01 = 3.00 x [tex]10^{10}[/tex] Hz

Therefore, the frequency of the microwave waves is approximately 3.00 x [tex]10^{10}[/tex] Hz.

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A two-pole AC motor operates on a three-phase, 60 Hz, 240 Vrms line-to-line supply.The answer is option B, 1800 rpm.

This is because the synchronous speed of a two-pole AC motor is given by the formula:

Synchronous speed (in RPM) = (120 x Frequency) / Number of poles

In this case, the frequency is 60 Hz and the number of poles is 2.

Synchronous speed = (120 x 60) / 2 = 3600 rpm

However, this is the theoretical speed that the motor would operate at if there was no load or slip. In reality, the motor will experience some slip, which means that its actual operating speed will be slightly less than the synchronous speed.

Therefore, the correct answer is option B, 1800 rpm, which is slightly less than the synchronous speed of 3600 rpm.

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The initial momentum of the golf ball is 2.40 kg⋅m/s. The average force exerted by the hood of the truck on the ball to stop it is [tex]-2.40 \times 10^4 N[/tex] and the time taken for the hood to stop the ball is [tex]1.00 \times 10^{-4} s[/tex]

a) The initial momentum of the golf ball can be calculated by using the formula:

p = mv

where m is the mass of the ball and v is the velocity of the ball. Plugging in the given values, we get:

p = (0.300 kg)(8.00 m/s) = 2.40 kg⋅m/s

Therefore, the initial momentum of the golf ball is 2.40 kg⋅m/s.

b) The average force exerted by the hood of the truck on the ball to stop it can be calculated using the formula:

[tex]F = \Delta p/ \Delta t[/tex]

where Δp is the change in momentum of the ball and Δt is the time taken for the ball to come to rest. Since the ball comes to rest, the final momentum of the ball is zero. So the change in momentum is:

[tex]\Delta p[/tex] = 0 - 2.40 kg⋅m/s = -2.40 kg⋅m/s

To find the time taken, we need to use the formula for distance traveled during a uniform deceleration:

[tex]d = (1/2)at^2[/tex]

where d is the distance traveled, a is the deceleration, and t is the time taken. The distance traveled by the ball can be taken as the dent made by the ball on the hood, which is 0.400 cm or 0.00400 m. The deceleration of the ball can be found by using the formula:

[tex]v^2 = u^2 + 2ad[/tex]

where u is the initial velocity (8.00 m/s), v is the final velocity (0 m/s), and d is the distance traveled (0.00400 m). Solving for a, we get:

[tex]a = (v^2 - u^2)/2d = -80,000 \;m/s^2[/tex]

(Note that the negative sign indicates that the ball is decelerating.)

Now we can find the time taken:

[tex]t = \sqrt{(2d/a)}[/tex]

[tex]t = \sqrt{(2 \times 0.00400\; m/80,000 \;m/s^2) }[/tex]

[tex]t = 1.00 \times 10^{-4} s[/tex]

So the average force exerted by the hood of the truck on the ball to stop it is:

[tex]F = \Delta p/ \Delta t[/tex]

[tex]F = (-2.40\; kg\;m/s)/(1.00 \times 10^{-4} s)[/tex]

[tex]F = -2.40 \times 10^4 N[/tex]

(Note that the negative sign indicates that the force is in the opposite direction to the motion of the ball.)

c) The time taken for the hood to stop the ball is [tex]1.00 \times 10^{-4} s[/tex], as found in part (b).

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The speed with which the harmonic wave travels in the wire is approximately 707.41 meters per second.

To find the speed of a harmonic wave traveling in a wire, we need to use the following formula:

Speed (v) = Wavelength (λ) * Frequency (f)

In this case, we are given the amplitude, wavelength, and frequency of the wave. The amplitude (2.51 mm) is not necessary to calculate the speed, so we can focus on the wavelength and frequency:

Wavelength (λ) = 1.09 m
Frequency (f) = 649 Hz

Now, we can use the formula to calculate the speed of the wave:

Speed (v) = 1.09 m * 649 Hz

Multiplying the wavelength and frequency together:

v = 707.41 m/s

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Answer:

3.6 MJ

Explanation:

1 kWh = 1 MJ

Remember that this is the same as the equation Power×time = Energy

Step 1: Convert kWh (kiloWatt×hour) to Ws (Watt×second)

1 kW = 1000 Watt

1 h = 60 min×60 sec = 3600 seconds

1000 W×3600s = 3600000 Joules

Divide 3600000 J by 10^6 to get 3.6 Mega Joules

The force between the two particles remains the same when both charges and the separation are doubled.

If the charge of each of the two particles is doubled and the separation between them is also doubled, the force between the two particles can be determined using Coulomb's Law:

F = (k * |q1 * q2|) / r^2

When both charges (q1 and q2) are doubled, the numerator becomes 4 * |q1 * q2|. And when the separation (r) is doubled, the denominator becomes (2r)^2 = 4r^2.

So, the new force (F') is:

F' = (k * 4|q1 * q2|) / (4r^2)

By canceling out the "4" in both numerator and denominator:

F' = (k * |q1 * q2|) / r^2

You'll notice that F' = F, which means the force between the two particles remains the same when both charges and the separation are doubled.

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One example of a role where gender shifts occur is politics. Women and non-binary individuals who enter the political sphere often experience a shift in their status and how they are treated by others. They may be viewed as less competent or capable than their male counterparts, or face discrimination and bias based on their gender identity. However, as more women and non-binary individuals are elected to political positions, there is a growing recognition of their abilities and contributions, and a shift towards greater gender equality in the political realm. Despite this progress, there is still much work to be done to address the systemic barriers that prevent women and non-binary individuals from fully participating in politics and achieving equal status and treatment.

The 60-kg player moves 3 meters with respect to the ice when the skaters have exchanged positions with respect to each other.

We can begin by using conservation of momentum to find the speed of the center of mass of the system. Since the system is initially at rest, the total momentum is zero. After the players start pulling themselves along the pole towards each other, they will move towards the center of mass of the system, which will move in the opposite direction to conserve momentum.

We can find the position of the center of mass by using the fact that the system is symmetric. The center of mass must be at the midpoint of the pole, or 5 m from either end.

Let's first find the velocity of the center of mass of the system:

total mass = 40 kg + 60 kg = 100 kg

momentum before = 0

momentum after = total mass × velocity of center of mass

velocity of center of mass = momentum after / total mass

velocity of center of mass = 0 / 100 kg

velocity of center of mass = 0 m/s

Since the velocity of the center of mass is zero, we know that the center of mass will remain in the same position throughout the motion of the players.

Now, let's consider the motion of the players. They will move towards each other with equal and opposite speeds, until they meet at the center of the pole. At this point, the 60-kg player will be moving in the direction of the 40-kg player with the same speed that the 40-kg player was initially moving.

Let's call the distance that the 60-kg player moves d. Then the distance that the 40-kg player moves is 10 m - d.

We can set up an equation to conserve momentum in the horizontal direction:

momentum before = momentum after

(40 kg)×(0 m/s) + (60 kg)×(0 m/s) = (40 kg)×(v) + (60 kg)×(-v)

where v is the speed of the players after they start moving towards each other. The negative sign in front of the 60-kg player's velocity indicates that the player is moving in the opposite direction to the 40-kg player.

Simplifying this equation, we get:

0 = 20 kg × v

v = 0 m/s

This means that the players come to a stop at the center of the pole.

Now we can find the distance that the 60-kg player moves, d:

d / 5 m = 60 kg / 100 kg

d = 3 m

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The distance among the two slits is 1.73 x 10⁻³ cm.

The third black fringe will appear 0.627 cm from the center of the dazzling fringe.

(a) The distance between the central bright fringe and the third bright fringe is given by:

Δy = (nλD) / d

where Δy is the distance between the central fringe and the nth bright fringe, λ is the wavelength of the light, D is the distance between the slits and the screen, and d is the distance between the slits.

Substituting the given values, we get:

3.11 cm = (1 x 632.8 nm x 85.0 cm) / d

Solving for d, we get:

d = (1 x 632.8 nm x 85.0 cm) / 3.11 cm = 1.73 x 10⁻³ cm

Therefore, the distance between the two slits is 1.73 x 10⁻³ cm.

(b) The distance between the central bright fringe and the nth dark fringe is given by:

Δy = [(2n - 1)λD] / (2d)

where Δy is the distance between the central fringe and the nth dark fringe, λ is the wavelength of the light, D is the distance between the slits and the screen, and d is the distance between the slits.

Substituting the given values and n=3, we get:

Δy = [(2 x 3 - 1) x 632.8 nm x 85.0 cm] / (2 x 1.73 x 10⁻³ cm) = 0.627 cm

Therefore, the third dark fringe will occur 0.627 cm away from the central bright fringe.

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A. the distance between the two slits is approximately 12.8 micrometers. B. the third dark fringe will occur at a distance of approximately 0.557 cm from the central bright fringe.

Slit is a term used to refer to a long, narrow opening or gap. It is most commonly used to describe a thin cut in a piece of material or a surface. Slits are used in a variety of fields, including engineering, manufacturing, and architecture.

A. The distance between the two slits can be calculated using the equation:
d sinθ = mλ
First, we need to calculate the wavelength of the light using the frequency:
[tex]\lambda = c/f = (3.00 \times 10^8 m/s) / (6.32 \times 10^{14} Hz) = 4.74 \times 10^{-7} m[/tex]
[tex]tan \theta = (3.11 cm) / (85.0 cm)[/tex]
[tex]\theta = tan^{-1} (3.11 cm / 85.0 cm) = 2.10^{\circ}[/tex]
Finally, we can substitute the values into the equation and solve for d:
[tex]d = m\lambda / sin\theta = (3)(4.74 \times 10^{-7} m) / sin(2.10^{\circ}) \approx 1.28 \times 10^-5 m = 12.8 \mu m[/tex]
Therefore, the distance between the two slits is approximately 12.8 micrometers.

B. The distance from the central bright fringe to the third dark fringe can be calculated using the equation:
[tex]y = (m + 1/2) (\lambda d)\\y = (m + 1/2) (\lambda D/d) = (3 + 1/2) (4.74 \times 10^{-7} m) (85.0 cm) / (12.8 \times 10^{-6} m) \approx 0.557 cm[/tex]
Therefore, the third dark fringe will occur at a distance of approximately 0.557 cm from the central bright fringe.

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The weight of the aquarium affects the amount of compression of each post. The heavier the aquarium, the more force it exerts on the posts, causing them to compress.

The amount of compression of each post depends on the weight of the aquarium, the size of the posts, and the type of material the posts are made from. For example, a heavier aquarium will compress wood posts more than metal posts of the same size.

Generally, the amount of compression of each post should be calculated by the weight of the aquarium divided by the number of posts. This number can then be used to determine the amount of compression of each post.

To ensure the posts remain secure, it is important to ensure the amount of compression does not exceed the post's maximum compression capacity.

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The average current in a 120 V power line to a house is typically around 15 amps, give or take a few amps depending on the power consumption of the household.

The average current in a 120 V power line to a house can vary depending on the power consumption of the household. However, we can use Ohm's law to calculate an estimate of the current. Ohm's law states that current is equal to voltage divided by resistance (I = V/R). In this case, we can assume that the resistance is equal to the resistance of the wiring, which is typically very low.

Using this formula, we can calculate the current as I = 120 V / R. The value of R can vary depending on the size and type of wiring used, but for residential wiring, it is typically around 0.1 ohms.

Therefore, I = 120 V / 0.1 ohms = 1200 amps.

However, it's important to note that this calculation assumes a very low resistance in the wiring and doesn't take into account the actual power consumption of the household. In reality, the current will vary based on the power being consumed by the appliances in the house.

In practice, the current will typically be much lower, usually in the range of 10-20 amps for an average household. It's important to note that the current can still spike much higher than this during power surges or when large appliances are turned on.

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Despite the fact that the moon is slightly larger than Pluto, the two bodies are vastly different, and their unique characteristics make them both interesting objects of study for astronomers and space scientists.

Yes, the way things work on Earth's moon would be different from the way they work on Pluto, despite the fact that Earth's moon is slightly larger than Pluto's. This is because the characteristics of a celestial body depend on various factors such as its size, mass, density, and distance from the sun.

One major difference between the two is the gravitational force. The gravitational force on the moon is about one-sixth of that on Earth, while on Pluto, it is about one-fifteenth of that on Earth. This means that objects on the surface of the moon would weigh less than those on Pluto, and they would also fall more slowly.

Another significant difference is the surface conditions. The moon has a relatively smooth surface with little atmosphere and extreme temperature variations, while Pluto has a much more rugged terrain, a thin atmosphere, and a much colder surface with temperatures reaching -240°C.

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Conductor, solar energy, power, solid wire, nonconductor or insulator power supply unit, stranded, conductor, fuse, LED , switch, may being described in each sentence.

The complete question is ,

Direction: Identify what is being described in each sentence. Write your answer on a separate sheet of paper. 1. It resists electricity, heat and sound. 2. It requires a source of energy for its operation.

3. It generates energy but can't dissipate energy.

4. It is a type of wire assembled in a single piece of metal.

5. It permits electrical current, heat and sound to flow freely.

6. It is a computer hardware responsible in supplying power.

7. It is made up of multiple small strands that make-up a single conductor

8. It is a safety device used to protect an electrical circuit from cxcessive current. 9. It is a semiconductor that illuminates when an electrical charge passes through it.

10. It is a device used to break an electric current and transfer it to another conductor.​

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The lower and upper half-power frequencies of the filter are both equal to 1 Hz.

A two-stage band-pass filter can be designed using two resistor-capacitor (RC) filter stages, as shown below(image attached):
In this circuit, the input voltage is applied to the first RC stage, consisting of R1 and C1, which is followed by a second RC stage consisting of R3 and C2. The output of the second stage is then fed to a load resistor RLoad.

The transfer function of this circuit can be found by analyzing each RC stage separately and then cascading their transfer functions. The transfer function of an RC stage is given by:

H(s) = 1 / (1 + sRC)

where s is the complex frequency variable and RC is the time constant of the RC circuit.

The transfer function of the first stage is:

H1(s) = 1 / (1 + sR1C1)

The transfer function of the second stage is:

H2(s) = 1 / (1 + sR3C2)

The overall transfer function of the two-stage band-pass filter is the product of the transfer functions of the two stages:

H(s) = H1(s) * H2(s)

Substituting the component values, we get:

H1(s) = 1 / (1 + s(1Ω)(1F)) = 1 / (1 + s)

H2(s) = 1 / (1 + s(1Ω)(1F)) = 1 / (1 + s)

H(s) = H1(s) * H2(s) = 1 / (1 + s)²

The frequency response of the filter is given by:

|H(jω)| = 1 / sqrt((1 - ω²)² + 4ζ²ω²)

where ω is the angular frequency, given by ω = 2πf, and ζ is the damping ratio, given by ζ = 1/2.

At the half-power frequencies, the magnitude of the transfer function drops to 1/√2 of its maximum value. Setting |H(jω)| = 1/√2 and solving for ω, we get:

ω1 = 1 / (R1C1) = 1 / (1Ω * 1F) = 1 rad/s

ω2 = 1 / (R3C2) = 1 / (1Ω * 1F) = 1 rad/s

As a result, the filter's bottom and upper half-power frequencies are both equal to 1 Hz.

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Your neighbor will finish cutting her lawn at 10:00 am, which is one hour after both of you started.

Since your lawn is twice as large as your neighbor's lawn, it takes you a certain amount of time to cut it, which we can analyze to determine when your neighbor will finish cutting her lawn.

You started cutting your lawn at 9:00 am and finished at 11:00 am. This means it took you 2 hours to complete the task. Since your neighbor's lawn is half the size of yours, it will take her half the amount of time to finish cutting her lawn, assuming you both exert the same force using the same self-propelled lawn mower.

To calculate the time it will take your neighbor to cut her lawn, simply divide your time (2 hours) by 2. This gives us 1 hour. Your neighbor started cutting her lawn at the same time you did, 9:00 am, and will take 1 hour to complete the task.

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Yes, the driver is accelerating when they put their foot on the gas pedal. Acceleration is the rate of change of velocity, which means that any change in speed or direction of motion is considered acceleration.

In this case, when the driver presses on the gas pedal, the car's velocity increases, causing a change in speed.

Therefore, the car is accelerating.

It's important to note that acceleration doesn't only refer to an increase in speed but can also refer to a decrease in speed or a change in direction, such as turning a corner.

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Answer: B. Temperature of water

Explanation:

An independent variable is "the variable that is changed or controlled in a scientific experiment or a mathematical or statistical model" and "It is the variable that the researcher chooses and that may affect the dependent variable"

The Temperature of the water is only affected by Jose thus it is a independent variable

The speed of Car A going relative to a passenger in Car B is 10mph

The relative speed of Car A and Car B since they are driving towards each other is given by;

V = 60+70=130mph

In order to find the speed of Car A going relative to a passenger in Car B we need to subract speed of car B.

vA/vB= va-vB

60-70= -10mph

The negative sign indicate that car A is travelling in opposite direction relative to car B.

Therefore, The speed of Car A going relative to a passenger in Car B is 10mph

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The centripetal force is 5,444.27 N, the average centripetal force exerted on a car is 6,988.31 N, the speed of the rider is 18.06 m/s, the speed of an electron is 1.73 x 10⁷ m/s, the force exerted by the Earth on a satellite is 1.84 x 10⁴ N, the maximum speed is 27.39 m/s and the speed of the bike is 27.39 m/s.

1. The centripetal force acting on a 925 kg car as it rounds an unbanked curve with a radius of 75 m at a speed of 22 m/s can be calculated using the formula [tex]Fc = (mv^{2} )/r[/tex]. Substituting the given values, we get [tex]Fc = (925 kg \times 22^{2} m^{2} / s^{2} ) / 75m[/tex] = 5,444.27 N.

2. To find the average centripetal force exerted on a car with a mass of 833 kg rounding an unbanked curve with a radius of 105 m at a speed of 28.0 m/s, we can use the same formula [tex]Fc = (mv^{2} )/r[/tex]. Substituting the given values, we get [tex]Fc = (833 kg \times 28.0^{2} m^{2} /s^{2} ) / 105 m[/tex] = 6,988.31 N.

3. The speed of the rider in an amusement park ride with a radius of 2.8 m and a time of one revolution of 0.98 s can be calculated using the formula [tex]v = 2\pi r / t[/tex]. Substituting the given values, we get[tex]v = (2 \times 3.14 \times 2.8 m) / 0.98 s[/tex] = 18.06 m/s.

4. The speed of an electron in a circle with a radius of [tex]2.00 \times 10^{-2} m[/tex] and a force  [tex]4.60 \times 10^{-14} N[/tex] acting on it can be calculated using the formula [tex]v = \sqrt{(Fcr / m)}[/tex]. Substituting the given values, we get

[tex]v = \sqrt{[(4.60 \times 10^{-14} N \times 2.00 x 10^{-2} m) / 9.11 \times 10^{-31} kg]}[/tex]

[tex]= 1.73 \times 10^7 m/s.[/tex]

5. The force exerted by the Earth on a satellite with a mass of [tex]2.7 \times 10^3[/tex] kg orbiting at a distance of [tex]1.8 \times 10^7[/tex] m and a speed of [tex]4.7 \times 10^3\;m/s[/tex]  can be calculated using the formula [tex]Fg = (Gm_{1} m_{2}) / r^{2}[/tex]. Substituting the given values, we get

[tex]Fg = (6.67 \times 10^{-11} N(m/kg)^2 \times 5.97 \times 10^{24} kg \times 2.7 \times 10^3 kg) / (1.8 \times 10^7 m)^{2}[/tex]

[tex]= 1.84 \times 10^4 N.[/tex]

6. The maximum speed at that a 2.0 kg mass can be whirled in a horizontal circle with a radius of 1.10 m before the string breaks, given a maximum force of 135 N that the string can withstand, can be calculated using the formula[tex]v = \sqrt(Fr / m)[/tex]. Substituting the given values, we get

[tex]v = \sqrt{[(135 N \times 1.10 m) / 2.0 kg]}[/tex]

= 16.47 m/s.

7. The speed of the bike in a motocross jump with a radius of 75.0 m, where the rider experiences apparent weightlessness due to the acceleration of the bike, can be calculated using the formula [tex]v = \sqrt{(rg)[/tex]. Substituting the given values, we get

[tex]v = \sqrt{(75.0\;m \times 9.81 m/s^{2} )}[/tex]

= 27.39 m/s.

In summary, these problems involve calculating various aspects of circular motion, including centripetal force, speed, and radius, using different formulas. The calculations involve substituting the

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Answer:

Both the vessels are likely to get heated up to the same temperature since they have the same quantity of water and are exposed to the same amount of sunlight. The color of the vessel (white or black) does not play a significant role in heating the water. However, it is worth noting that black absorbs more light and heat than white due to its higher emissivity and lower reflectivity, but the effect is negligible in this scenario because the water inside the vessels will absorb most of the sunlight regardless of the vessel's color.

Answer:

The black vessel will heat up faster.

Explanation:

When light falls on an object, it can either be absorbed, reflected, or refracted through the object. The color of an object is determined by the wavelengths of light that it absorbs and reflects. A black object appears black because it absorbs all wavelengths of visible light, whereas a white object appears white because it reflects all wavelengths of visible light.

In the case of the two vessels, the black vessel absorbs more of the light and heat from the sun than the white vessel. This is because the black pigment in the paint absorbs a wider range of wavelengths of visible and non-visible light. As a result, more of the energy from the sun is converted into heat, raising the temperature of the water inside the vessel.

In contrast, the white vessel reflects most of the light and heat from the sun, resulting in less energy being absorbed by the water inside the vessel. This is because the white pigment in the paint reflects a wide range of wavelengths of visible light, including the higher energy wavelengths in the ultraviolet and infrared range that contribute to the heating of the vessel.

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Answer: The various possible standing waves on a string are called Harmonics (or resonant modes). Harmonics are the frequencies of the standing waves that are produced when a string is plucked or struck. The harmonics are also sometimes referred to as overtones or partials. The nodes and antinodes are the points on the string where there is no displacement and maximum displacement respectively. The incident waves are the initial waves that are set up on the string before any reflections occur.

Explanation:

The various possible standing waves on a string are called Harmonics (or resonant modes).

Standing waves occur when two waves with the same frequency, amplitude, and wavelength travel in opposite directions and interfere with each other. This interference creates a unique pattern with specific points called Nodes and Antinodes.
Nodes are points on the string where the displacement is always zero, meaning they do not move. These points occur when the two waves perfectly cancel each other out.
Antinodes, on the other hand, are points on the string where the displacement is maximum. These points occur when the two waves perfectly reinforce each other, resulting in the greatest possible amplitude.
Harmonics (or resonant modes) are the different frequencies at which a string can support standing waves. The fundamental frequency, or first harmonic, is the lowest frequency at which a standing wave can form. Higher harmonics, or overtones, are multiples of the fundamental frequency and create more complex standing wave patterns.

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An increase in potential difference (P.D.) across a thermistor leads to an: increase in current flow, which generates heat and raises the temperature of the thermistor.

A thermistor is a temperature-sensitive resistor whose resistance varies with temperature changes. When the potential difference (P.D.) across a thermistor increases, more electric current flows through it. As the electric current increases, the electrons in the thermistor gain more kinetic energy and collide more frequently with the lattice structure of the material, which generates heat.

The increased heat raises the temperature of the thermistor. In a negative temperature coefficient (NTC) thermistor, the resistance decreases as the temperature rises. This is because, as the thermistor heats up, the lattice structure of the material expands, allowing more electrons to move more freely and conduct electricity more efficiently. Consequently, the resistance decreases with an increase in temperature.

So, to summarize, an increase in potential difference (P.D.) across a thermistor leads to an increase in current flow, which generates heat and raises the temperature of the thermistor. In an NTC thermistor, this increased temperature causes a decrease in resistance due to the expansion of the lattice structure, which allows electrons to move more freely and conduct electricity more efficiently.

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The number of turns needed on the secondary coil is 45. The transformer is a device that transfers electrical energy from one circuit to another through electromagnetic induction.

In order to determine the number of turns needed on the secondary coil of the transformer, we need to use the equation:

Vp/Vs = Np/Ns

Where Vp is the potential difference on the primary coil, Vs is the potential difference on the secondary coil, Np is the number of turns on the primary coil, and Ns is the number of turns on the secondary coil.

We know that Vp is 1.5V and Vs is 5.0V. We also know that Np is 150. So, we can rearrange the equation to solve for Ns:

Ns = (Vp/Vs) x Np

Ns = (1.5V/5.0V) x 150

Ns = 45

Therefore, the number of turns needed on the secondary coil is 45. The transformer is a device that transfers electrical energy from one circuit to another through electromagnetic induction. The voltage ratio between the primary and secondary coils is determined by the ratio of the number of turns in each coil.

In this case, we are given the input and output voltages and the number of turns on the primary coil, and we use this information to calculate the number of turns needed on the secondary coil.

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M. Bouc suspects Gino Foscarelli as the murderer due to Ratchett stealing Foscarelli's car, insults, hot temper, and possible mafia connections. The correct options are A, B, C, and E.

In Agatha Christie's "Murder on the Orient Express," M. Bouc believes that the Italian, Gino Foscarelli, is the murderer based on several reasons. Firstly, Ratchett had stolen a car from Foscarelli, indicating a possible motive for revenge.

Secondly, Ratchett had insulted Foscarelli, which could have provoked him to commit the crime. Additionally, Foscarelli's hot temper made him a likely suspect. Furthermore, M. Bouc believes that Foscarelli is a member of the mafia, which implies that he has the capability to carry out such a crime.

However, these reasons are not enough to make a conclusive argument for Foscarelli's guilt. The evidence against Foscarelli is based on assumptions, and Poirot highlights that the clues and motives are too obvious and simple.

Ultimately, the real motive and identity of the murderer are much more complex than initially anticipated. Therefore, M. Bouc's belief that Foscarelli is the murderer may not be entirely accurate.

In summary, M. Bouc believes that Foscarelli is the murderer due to several reasons, such as a possible motive for revenge and a hot temper. However, these reasons are not enough to make a conclusive argument for Foscarelli's guilt, and the real motive and identity of the murderer are much more complex. Therefore, the correct options are A, B, C, and E.

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Two large speakers broadcast the sound of a band tuning up before an outdoor concert.While the band plays an A whose wavelength is 0. 773 m, Brenda walks to the refreshment stand along a line parallel to the speakers. If the speakers are separated by 12. 0 m and Brenda is 24. 0 m away then 0.387 meters must she walk between the "loudspots".

Since the wavelength of the sound wave is known, we can use the concept of interference to find the distance between the "loudspots". At the point of maximum constructive interference, the waves from both speakers will add up, creating a louder sound. At the point of maximum destructive interference, the waves will cancel each other out, creating a quieter sound.

Let d be the distance that Brenda needs to walk to reach the point of maximum constructive interference between the two speakers. At this point, the waves from both speakers will add up to create a louder sound. The path difference between the waves from the two speakers at this point will be exactly one wavelength.

Using the Pythagorean theorem, we can find the distance between Brenda and each of the speakers:

Distance from Brenda to speaker 1 = [tex]\sqrt{24^{2} +6^{2} }[/tex] = 24.6 m

Distance from Brenda to speaker 2 = [tex]\sqrt{24^{2}+18^{2} }[/tex]= 30 m

The path difference between the waves from the two speakers at the point of maximum constructive interference will be:

Path difference = distance from Brenda to speaker 2 - distance from Brenda to speaker 1

Path difference = 30 m - 24.6 m = 5.4 m

Since the path difference is exactly one wavelength, we have

Wavelength = path difference = 0.773 m

Therefore, the distance that Brenda needs to walk to reach the point of maximum constructive interference is

d = wavelength/2 = 0.773 m/2 = 0.387 m

So Brenda needs to walk 0.387 meters between the "loudspots".

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