Here, the total momentum before and after the release of the projectile is same. From this concept the final velocity of the cannon after the release will be 0.00433 m/s.
What is conservation of momentum ?Momentum of an object is the product of its mass and velocity. During a collision, the momentum after and before the collision is constant. This can be applied in the case of a projectile from the cannon.
Here, the initial momentum of the cannon and the ball is zero, because they are at rest.
After, projectile the total momentum momentum is zero itself according to conservation of momentum.
momentum of the ball = 0.05 kg × 0.1 m/s cos 30 + 1 kg × v = 0
Here v is the velocity of the cannon.
then v = 0.05 kg × 0.1 m/s cos 30 / 1 kg
= 0.0043 m/s.
Therefore, the velocity of the cannon after the projectile is released is 0.0043 m/s.
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Have average hpurly earnings in the United States increased sinced 1980? Answer question using the words nominal and real .
Yes, the average hourly earnings in the United States have increased since 1980, both nominal wages and in real terms.
What are nominal wages?
Nominal wages refer to the actual dollar amount earned, without any adjustments for inflation. When looking at nominal wages, we can see that the average hourly earnings in the United States have indeed increased since 1980. According to data from the Bureau of Labor Statistics, the average hourly earnings for all employees in the private sector was $3.10 in 1980, and has since increased to $31.73 in 2021.However, inflation has also been a factor during this time period, meaning that the purchasing power of a dollar has decreased over time. Real wages take into account the effects of inflation, allowing us to compare earnings over time in terms of purchasing power. When we adjust for inflation using a measure like the Consumer Price Index (CPI), we can see that while the nominal wage has increased, the real wage has not increased as much. In other words, even though workers are earning more in nominal terms, their earnings have not kept pace with the rising cost of living.So, while both nominal and real wages have increased since 1980, the extent to which they have increased depends on the measure used.To know more about nominal wages, click the link given below:
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Please help (50 points and Brainly)
Answer:
the asnsweis wavew
Explanation:
i just need rge points tbh
What is a type of potential energy that a marshmallow has if the marshmallow is sitting in the bag
Answer:
potential until moved than kinetic
Explanation:
If you move 2 newtons of mess for 5 meters how much work did you do?
Answer: If the force is applied at an angle to the displacement, the work is W = fd cosθ Given: The force acting, F = 5 Newtons, The displacement of the object, d = 2 meters. Calculate the work done by the formula given below, W = Here, W is the work done. Substitute the values, W = 5 * 2 W = 10 Joules
Explanation:
In the first 20.0 seconds of flight, the Saturn V rocket achieved an altitude of 510 m, and a velocity of 56 m/s. The rocket weighed approximately 2.77∗10^6 kg. What was the average power produced by the rocket?
7.0∗10^9 W
1.8∗10^10 W
9.1∗10^8 W
2.6∗10^8 W
Answer:
We can use the work-energy theorem to find the average power produced by the rocket:
Work done = Change in kinetic energy = (1/2)mv_f^2 - (1/2)mv_i^2
where m is the mass of the rocket, v_f is the final velocity, and v_i is the initial velocity.
From the given information, we have:
m = 2.77*10^6 kg
v_f = 56 m/s
v_i = 0 m/s
Using the kinematic equation for displacement:
y = v_i*t + (1/2)at^2
where y is the displacement (altitude), t is the time, and a is the acceleration.
We can rearrange this equation to solve for a:
a = 2y/t^2 = 2(510 m)/(20.0 s)^2 = 1.275 m/s^2
Then, we can use the kinematic equation for velocity:
v_f = v_i + at
v_f = 0 m/s + (1.275 m/s^2)(20.0 s) = 25.5 m/s
Now we can calculate the work done by the rocket:
Work done = (1/2)(2.7710^6 kg)(25.5 m/s)^2 - (1/2)(2.7710^6 kg)(0 m/s)^2 = 9.065*10^8 J
Finally, we can calculate the average power produced by the rocket:
Average power = Work done / Time taken = 9.06510^8 J / 20.0 s = 4.5310^7 W
Therefore, the average power produced by the rocket was approximately 4.53*10^7 W.
The answer is: 9.1∗10^8 W.
Explanation:
If I use _____, ________, and _______, then I can make ______ new elements in 5 minutes.
If I use copper wire, magnets, and a battery, then I can make an electromagnet as a new element in 5 minutes.
What is the battery?
An apparatus that transforms chemical energy into electrical energy is a battery. It is typically composed of one or more electrochemical cells that use a chemical reaction to generate a flow of electrons, which produces an electric current.
Batteries are used in a wide variety of applications, from powering small electronic devices like flashlights and remote controls to providing backup power for homes and businesses. They come in many different shapes, sizes, and types, including disposable batteries that are used once and then discarded, and rechargeable batteries that can be reused multiple times by recharging their chemical components.
This sentence refers to the creation of an electromagnet using copper wire, magnets, and a battery. An electromagnet is a type of magnet that is created by running an electrical current through a coil of wire.
To create an electromagnet using copper wire, magnets, and a battery, you would need to take the following steps:
1. Wrap the copper wire around a piece of iron or steel, such as a nail, to create a coil. The more turns of wire you have in the coil, the stronger the electromagnet will be.
2. Connect the ends of the wire to the battery, making sure that the positive (+) and negative (-) terminals are connected to the correct ends of the wire. This will create a flow of electrical current through the wire.
3. Hold the magnet next to the iron or steel core. The magnetic field of the magnet will induce a magnetic field in the iron or steel core, which will in turn create a stronger magnetic field in the coil of wire.
4. You now have an electromagnet that will remain magnetized as long as the current is flowing through the wire.
Therefore, the process of creating an electromagnet using copper wire, magnets, and a battery is a simple and effective way to produce a magnet for a variety of applications. It can be used in many devices, including doorbells, motors, and speakers, among others.
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Which statement best describes the conditions created by El Niño?
Responses
Winds that normally blow to the east slacken, waters off the coast of North America warm up, and upwelling decreases, reducing the nutrients in the water.
Winds that normally blow to the east slacken, waters off the coast of North America warm up, and upwelling decreases, reducing the nutrients in the water.
Winds that normally blow to the west slacken, waters off the coast of South America warm up, and upwelling decreases, reducing the nutrients in the water.
Winds that normally blow to the west slacken, waters off the coast of South America warm up, and upwelling decreases, reducing the nutrients in the water.
Winds that normally blow to the west get stronger, waters off the coast of South America cool down, and upwelling increases, improving the nutrients in the water.
Winds that normally blow to the west get stronger, waters off the coast of South America cool down, and upwelling increases, improving the nutrients in the water.
Winds that normally blow to the east get stronger, waters off the coast of North America cool down, and upwelling increases, improving the nutrients in the water.
Winds that normally blow to the west slacken, waters off the coast of South America warm-up, and upwelling decreases, reducing the nutrients in the water. Option 3.
What is El NinoEl Niño is a natural climate phenomenon that occurs in the Pacific Ocean, characterized by the warming of the ocean surface water, which causes changes in wind patterns and weather worldwide.
During El Niño, the normal trade winds weaken, which can lead to droughts, flooding, and other weather extremes in various parts of the world.
El Niño events typically occur every two to seven years and can last for several months to a few years.
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Answer: 3. Winds that normally blow to the west get stronger, waters off the coast of South America cool down, and upwelling increases, improving the nutrients in the water.
A man pushed a table, using a force of 8 newtons. He moved the table 2 meters. How much work did he do?
The man did 16 Joules of work on the table.
What is the amount of work done by the man?Work done is simply defined as the energy transfer that takes place when an object is either pushed or pulled over a certain distance by an external force. It is expressed as;
Work done = force × distance
Where force is the amount of force applied and distance is the distance the object was moved.
In this case;
Force applied = 8 newtonsDistance moved = 2 meters.So, substituting these values into the formula, we get:
Work done = force × distance
Work done = 8N × 2m
Work done = 16Nm
Work done = 16 Joules
Therefore, the work done on the table is 16J.
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Dan was in a roller coaster cart at the top of a hill, which was the tallest point on the ride. As the cart rushed down the hill, Dan screamed and put his hands up. The cart gained speed until it reached the bottom of the hill, where it was moving the fastest. Dan saw that the cart was headed toward a loop. He held on tight while the cart zoomed up and around the loop.
When was the most gravitational potential energy stored between the cart and Earth? Assume that the cart's mass did not change.
smallest possible potential energy The potential energy of the cart began to rise once more as it advanced higher up the loop as it entered the loop, but it was never able to match its level at the top of the hill.
What does children's potential energy entail?Potential energy is the energy that is held in reserve by an object due to its position or condition. Potential energy exists in objects like a spring stretched out, a bicycle on a hilltop, and a book held above your head.
What is potential and kinetic energy?On the other hand, kinetic energy is the energy of an object or a system's particles in motion .The most gravitational potential energy between the cart and the Earth was stored at the top of the hill, which was the tallest point on the ride where the cart was stationary. When the cart was at the top of the hill, it had the highest potential energy due to its position above the ground. As the cart began to move downhill, some of this potential energy was converted into kinetic energy, which increased the cart's speed.
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Seismic waves, known as P – waves, and S – waves can be use to study the earths interior, which otherwise would have be been impossible to explore. Which properties of P Dash and S – waves allow the study of earths interior.
(Multiple choice)
A. They travel at varying speeds, depending on the composition of layer.
B. They deflected while passing through layers of different compositions.
C. They are produced during earthquakes and volcanic eruptions.
D S – waves cannot pass through a layer of liquid composition
a bag of same size small balls contain 6 blue balls 5 red balls 5 yellow balls and 4 green balls what is the probality of selecting a blue or green ball on first draw
Answer:
Below
Explanation:
Blue ( 6) OR green ( 4) is 10 out of ( 6 + 5 + 5 + 4)
10 / 20 = 1/2 chance of blue OR green
A 1325 kg car and a 2050 kg pickup truck approach a curve on a highway that has a radius of 255 m. The curve is banked at 24.18 degrees so the vehicles can safely round it regardless of the condition of the tires.
A. As the car round the curve at 75.0 mi/h, find the normal force on the car due to the highway surface.
B. As the truck round the curve at 75.0 mi/h, find the normal force on the truck due to the highway surface.
The normal force on the truck due to the highway surface is 18109.26 N.
What is Centripetal force?Centripetal force is the force that is directed towards the center of a circular path that keeps an object moving along that path. It is given by the equation:
Fc = mv²/r
where Fc is the centripetal force, m is the mass of the object, v is its velocity, and r is the radius of the circular path.
First, we need to convert the speed from miles per hour to meters per second:
75.0 mi/h = 33.5 m/s
Next, we can use the centripetal force equation:
F_c = (m*v²)/r
where F_c is the centripetal force, m is the mass of the vehicle, v is the velocity of the vehicle, and r is the radius of the curve.
We can find the angle of the banked curve in radians:
θ = tan⁻¹(v²/(r*g))
where g is the acceleration due to gravity, which is approximately 9.8 m/s².
A. For the car:
m = 1325 kg v = 33.5 m/s r = 255 m θ = tan⁻¹(v²/(r*g)) = tan⁻¹((33.5 m/s)² / (255 m * 9.8 m/s²) = 0.49 radians
The normal force on the car is given by:
N = mgcos(θ) + F_c*sin(θ)
where N is the normal force and cos(θ) and sin(θ) are the components of the gravitational force and the centripetal force, respectively, parallel and perpendicular to the surface of the road.
Plugging in the values, we get:
N = (1325 kg * 9.8 m/s² * cos(0.49)) + ((1325 kg * (33.5 m/s)²) / (255 m) * sin(0.49)) N = 12434 N
Therefore, the normal force on the car due to the highway surface is 12434 N.
B. For the truck:
m = 2050 kg v = 33.5 m/s r = 255 m θ = tan⁻¹(v²/(r*g)) = tan⁻¹((33.5 m/s)² / (255 m * 9.8 m/s²)) = 0.49 radians
The normal force on the truck is given by:
N = mgcos(θ) + F_c*sin(θ)
Plugging in the values, we get:
N = (2050 kg * 9.8 m/s² * cos(0.49)) + ((2050 kg * (33.5 m/s)²) / (255 m) * sin(0.49)) N = 18109.26 N
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Someone Anyone Please help me?
The average velocity of the skier is 13.3 m/min East.
option A.
What is the average velocity of the skier?Average velocity is a measure of how fast an object has moved over a given period of time in a specific direction.
It is calculated as the displacement of an object divided by the time interval during which the displacement occurs.
Displacement is the straight-line distance between the object's initial and final positions, in a specific direction.
The formula for average velocity is:
Average Velocity = Displacement / Time
Average velocity of the skier = ( 40 m - 0 m ) / ( 3 min )
Average velocity of the skier = 13.3 m/min east
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What do I have to do on these help me out
Momentum After ∞ The velocity of the truck after the collision is 10m/s.
What is velocity ?Velocity is a vector quantity that measures the rate of change of an object's position with respect to time. It is a physical quantity that describes both the speed and direction of an object's motion. Velocity is the rate of change of an object's position, and is equal to the total distance traveled divided by the total time it took to travel that distance. It is represented by the symbol v, and its SI unit is m/s. Velocity is an important concept in physics, as it is used to describe the motion of objects in the universe.
This is because the total momentum before the collision (5000kg*20m/s) is equal to the total momentum after the collision (5000kg*10m/s + 1200kg*0m/s). So, the velocity of the truck after the collision is equal to 10m/s.
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Which type of wave has a wave perpendicular to the disturbance?
A. mechanical
B. transverse
C. surface
D. longitudinal
Answer:
B. transverse
Explanation:
The type of wave that has a perpendicular wave to the disturbance is transverse wave
instrument used to measure earthquake
Answer:
seismograph
Explanation:
seismograph
Answer:
seismometers and seismograph
Explanation:
this instrument respond to ground noise and shake like quake and volcanoes eruption
1. Osmium is the densest metal on earth. It has a density of 22.61 g.cm³. Which of the following best represents this density in kg.m³?
Answer: 2.72
Explanation: if this is not correct I don't know what to tell you other than don't use for answers and instead LEARN
What indicates that two objects are in thermal equilibrium? The objects ar the same size the objects abtounchingneach other the objects have the same temperature temperatures are changing
A projectile is shot up vertically with a velocity of 100ms-1 .How long does it take the projectile to reach a height of 375m?
Answer:
Explanation:
The motion of the projectile can be modeled using the following kinematic equation:
h = vi*t + (1/2)at^2
where h is the height of the projectile, vi is the initial velocity, a is the acceleration due to gravity (approximately -9.8 m/s^2), and t is the time elapsed.
We want to find the time it takes for the projectile to reach a height of 375 m, so we can set h = 375 and solve for t:
375 = 100t + (1/2)(-9.8)*t^2
Simplifying and rearranging, we get:
4.9t^2 + 100t - 375 = 0
We can solve this quadratic equation using the quadratic formula:
t = (-b ± sqrt(b^2 - 4ac)) / (2*a)
where a = 4.9, b = 100, and c = -375.
Plugging in the values, we get:
t = (-100 ± sqrt(100^2 - 44.9(-375))) / (2*4.9)
Simplifying, we get:
t = (-100 ± sqrt(10000 + 7350)) / 9.8
t = (-100 ± sqrt(17350)) / 9.8
We take the positive value of t, since we are only interested in the time it takes for the projectile to reach a height of 375 m:
t = (-100 + sqrt(17350)) / 9.8
t ≈ 21.43 seconds (rounded to two decimal places)
Therefore, it takes the projectile approximately 21.43 seconds to reach a height of 375 m.
The following image shows an eraser being measured by a ruler.
Eraser next to a centimeter ruler. Left edge is on the zero line and the right end lines up between the sixth seventh tick mark on the ruler after the fourth centimeter.
What is the length of the eraser in the picture? Explain how you came up with that value.
How many significant digits are associated with the measurement you provided in part a?
The length of the eraser is 4.6 cm. There are two significant figures in the measurement.
What is measurement of length?Measurement of length is the process of determining the distance between two points or the size of an object using standard units of length. The most commonly used unit of length in the International System of Units (SI) is the meter, which is defined as the distance traveled by light in a vacuum during a specific time interval.
In addition to the meter, other units of length are also used in different countries and applications.
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A particle has a charge of q = +4.7 μC and is located at the origin.
(a) When the particle is stationary, it will only experience a force due to the electric field. The force is given by:
F = qE
where q is the particle's charge as well as E is the electric field.
Substituting the given values, we have:
F = (4.9 × 10⁻⁶ C)(242 N/C) = 1.19 × 10⁻³N
The net force is directed in the +x direction.
What is magnetic force?Magnetic force is the force that arises between two magnetic objects or between a magnetic object and a moving charged particle. It is one of the four fundamental forces of nature, the others being the strong nuclear force, the weak nuclear force, and gravity.
The magnetic force is caused by the interaction between magnetic fields. When two magnetic objects are brought near each other, their magnetic fields interact and exert a force on each other.
(b) When the particle is moving along the +x axis at a speed of 345 m/s, it will experience both electric and magnetic forces. The electric force will be the same as in part (a). The Lorentz force equation may be utilized to calculate magnetic force:
F = q(v x B)
where v is the particle's velocity and B is the magnetic field.
Substituting the given values, we have:
F = (4.9 × 10⁻⁶ C)(345 m/s)(1.9 T) = 3.28 × 10⁻³ N
The right-hand rule can be used to determine the direction of the magnetic force. If you point your thumb in the direction of the velocity vector (+x axis) and your fingers in the direction of the magnetic field vector (+x and +y axes), your palm will face in the direction of the magnetic force vector, which is in the +z direction.
Therefore, the net force on the particle is given by the vector sum of the electric and magnetic forces:
Fnet = (1.19 × 10⁻³ N) + (3.28 × 10⁻³ N) = 4.47 × 10⁻³ N
The net force is directed in the +z direction.
(c) When the particle is moving along the +z axis at a speed of 345 m/s, it will only experience a magnetic force. The magnetic force can be calculated using the same equation as in part (b):
F = q(v x B)
where v is the particle's velocity and B is the magnetic field.
Substituting the given values, we have:
F = (4.9 × 10⁻⁶ C)(345 m/s)(1.9 T) = 3.28 × 10⁻³ N
The right-hand rule can be used to determine the direction of the magnetic force. If you point your thumb in the direction of the velocity vector (+z axis) and your fingers in the direction of the magnetic field vector (+x and +y axes), your palm will face in the direction of the magnetic force vector, which is in the -y direction.
Therefore, the net force on the particle is given by the magnetic force:
Fnet = 3.28 × 10⁻³ N
The net force is directed in the +y direction.
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1.3.2 Quiz. what is another way to describe the vector below? "40 feet to the right"
The vector described as "40 feet to the right" can also be expressed as a displacement vector. It represents the change in position of an object as it moves from one point to another.
Specifically, the vector denotes a horizontal displacement of 40 feet in the positive x-direction from the starting point.
Another way to describe the vector is to use a coordinate system. If we place the starting point at the origin (0,0) and define the x-axis to be the horizontal direction and the y-axis to be the vertical direction, then the vector can be represented as (40,0), where the first number corresponds to the x-coordinate and the second number corresponds to the y-coordinate. This notation emphasizes the fact that the vector has no vertical displacement, only a horizontal displacement of 40 feet.
Alternatively, we could describe the vector using magnitude and direction. The magnitude of the vector is simply its length, which in this case is 40 feet. The direction of the vector can be described as "to the right" or "in the positive x-direction." This notation is useful when comparing vectors with different magnitudes but the same direction or vice versa.
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Urgent!!! big brain needed!
A 66.4 kg person sits on the right end of a seesaw, 2.35 m from the fulcrum. On the other end, how far from the fulcrum should a 84.2 kg person sit to balance the seesaw?
1.92 m
1.85 m
2.08 m
1.61 m
1.85 m if On the right side of a seesaw, 2.35 meters from the fulcrum, a 66.4 kg individual is seated. How far away from the fulcrum on the opposite end should an 84.2 kg.
The correct statement is B.
What is a fulcrum with an example?For those who are unsure of what a fulcrum is, The answer to the question a fulcrum is the fixed point of a lever. A seesaw, for instance, is a lever with a fulcrum with in middle. The fulcrum of a seesaw is the stationary central component.
What are a pivot and a fulcrum?• The lever's pivot or turning point, or fulcrum. • The load, or the items you are attempting to transport. • The force, or the energy expended in moving the weight. With the help of a lever, you can move a heavy object with little effort. A lever is easier to move the farther away the effort (or force) comes from the fulcrum.
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Please help (50 points and Brainly)
Dantes peak 1997: the scientists know an eruption is immanent because the _____ are swarming and the ______ readings increase.
The scientists in the 1997 film "Dante's Peak" know an eruption is coming because of "rats" are congregating as well as the "sulfur dioxide" measurements are rising.
Is the mountain Dante's Peak real?Peak Dante | 1997 Wallace, located in Idaho's Western Rockies in the Bitteroot Alps, serves as the model for the fictional hamlet of "Dante's Peak". Digitally added elements include "Dante's Peak" and the surrounding alpine environment. The setting for Michael Cimino's novel Heaven's Gate was Wallace.
A failure, Dante's Peak?Dante's Peak may not have been warmly accepted at the time as it was treated seriously. It was a dreadful bomb that barely made $175 million just at movie office, like its rival Volcano.
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If an object continues to accelerate, what happens to its speed?
If an object continues to accelerate, the speed of the object will also increase.
What is acceleration?Acceleration is the amount by which a speed or velocity increases (and so a scalar quantity or a vector quantity).
The relationship between acceleration and speed is direct.
If the speed is increasing, the car has positive acceleration. When the car slows down, the speed decreases. The decreasing speed is called negative acceleration
Therefore, as the object continues accelerating, the speed increases.
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URGENT HELP NEEDED!!!
During basketball practice, two basketballs are rolling towards each other. Ball A has a velocity of 3.3 m/s east, and ball B has a velocity of 1.6 m/s west. Both balls have a mass of 0.62 kg. If ball B has a velocity of 1.2 m/s east after the collision, what is the velocity of ball A after the collision?
3.7 m/s west
0.5 m/s west
3.7 m/s east
0.5 m/s east
Since the initial velocity of ball A was 3.3 m/s east and the velocity of ball A after the collision is 6.7 m/s east, the velocity of ball A after the collision is 3.7 m/s east.
What is velocity?Velocity is a vector quantity that measures the rate and direction of an object's motion. It can be determined by measuring the displacement of the object over a certain period of time. Velocity is usually expressed in terms of distance per unit of time, such as meters per second (m/s). In physics, velocity is a fundamental concept that is used to describe the motion of objects.
The velocity of ball A after the collision can be calculated using the conservation of momentum equation. The equation is as follows:
m1v1 + m2v2 = m1v1' + m2v2'
where m1 is the mass of ball A, v1 is the initial velocity of ball A, m2 is the mass of ball B, v2 is the initial velocity of ball B, m1' is the mass of ball A after the collision, v1' is the velocity of ball A after the collision, m2' is the mass of ball B after the collision, and v2' is the velocity of ball B after the collision.
In this problem, the equation is:
(0.62 kg)(3.3 m/s east) + (0.62 kg)(1.6 m/s west) = (0.62 kg)(v1') + (0.62 kg)(1.2 m/s east)
We can solve this equation for v1':
(0.62 kg)(3.3 m/s east) + (0.62 kg)(1.6 m/s west) = (0.62 kg)(v1') + (0.62 kg)(1.2 m/s east)
0.62(3.3 + 1.6) = 0.62v1' + 0.74
4.9 = 0.62v1' + 0.74
4.9 - 0.74 = 0.62v1'
4.16 = 0.62v1'
v1' = 6.7 m/s east
Since the initial velocity of ball A was 3.3 m/s east and the velocity of ball A after the collision is 6.7 m/s east, the velocity of ball A after the collision is 3.7 m/s east.
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5. On Earth, where is hydrogen not found?
• A. Mine
• B. Natural gas well
• C. Water
O D. Atmosphere
Answer:
Atmosphere
Explanation:
Hydrogen,
H
2
, is one of the lightest gases that can be found on Earth. The other gas is helium, and these two gases are both lighter than air, because they have a high degree of buoyancy.
This means that the air below it is pushing up with a greater force than the air above it is forcing it down.
if the friction force of an object is -210 and the sum of forces is 190 what is the applied force
Answer:
If the friction force on an object is -210 N and the net force acting on the object is 190 N, then we can use the formula:
Net force = Applied force - Friction force
Solving for the applied force, we get:
Applied force = Net force + Friction force
Substituting the given values, we get:
Applied force = 190 N + (-210 N)
Applied force = -20 N
Therefore, the applied force on the object is -20 N. This means that the direction of the applied force is opposite to the direction of motion of the object.
Explanation:
The figures show a hypothetical planetary system at two different times. The system has a star S and three planets, labeled A, B, and C. The table provides the mass of each body in the system, as well as their spatial coordinates (,)
in their initial and final positions. The spatial coordinates of the bodies are given in Astronomical Units (AU).
Body Mass (kg) Initital Position Final Position
S S=2.0197×1030
(0,0)
(S,S)
A A=2.5623×1028
(0.1119,0)
(0,−0.2381)
B B=6.2841×1026
(0.3751,1.2975)
(−1.9117,0)
C C=8.6951×1027
(0,1.4245)
(−0.8865,−0.8445)
The initial velocity of the center of mass of the system is zero.
Find the magnitude S
of the star's displacement from the origin in its final position.
The magnitude S of the star's displacement from the origin in its final position is approximately 1.9117 AU.
What are Astronomical Units?Astronomical Units (AU) are a unit of distance commonly used in astronomy to measure distances within our solar system. One AU is defined as the average distance between the Earth and the Sun, which is approximately 93 million miles or 149.6 million kilometers.
To find the magnitude S of the star's displacement from the origin in its final position, we can use the distance formula:
distance = square root of ((x2 - x1)² + (y2 - y1)²)
where (x1, y1) are the initial coordinates of the star and (x2, y2) are the final coordinates of the star.
In this case, the initial coordinates of the star are (0, 0) and the final coordinates of the star are (S, S). We don't know the value of S yet, but we can use the fact that the initial velocity of the center of mass of the system is zero to find it.
The center of mass of the system can be found using the formula:
(m₁x₁ + m₂x₂ + m₃x₃) / (m₁ + m₂ + m₃)=x cm
(m₁y₁ + m₂y₂ + m₃y₃) / (m₁ + m₂ + m₃)=ycm
where m₁, m₂, and m₃ are the masses of the star and the two planets, and (x₁, y₁), (x₂, y₂), and (x₃, y₃) are their initial coordinates.
Using the values from the table, we can calculate the center of mass of the system:
x_cm = (2.0197×10³⁰ * 0 + 2.5623×10²⁸ * 0.1119 + 6.2841×10²⁶ * 0.3751 + 8.6951×10²⁷ * 0) / (2.0197×10³⁰ + 2.5623×10²⁸ + 6.2841×10²⁶ + 8.6951×10²⁷) ≈ 0.0038 AU
y_cm = (2.0197×10³⁰ * 0 + 2.5623×10²⁸ * 0 + 6.2841×10²⁶ * 1.2975 + 8.6951×10²⁷ * 1.4245) / (2.0197×10³⁰ + 2.5623×10²⁸ + 6.2841×10²⁶ + 8.6951×10²⁷) ≈ 1.3019 AU
Since the initial velocity of the center of mass is zero, the final velocity must also be zero. This means that the final position of the center of mass must be the same as the initial position.
Setting (x_cm, y_cm) in the final position to (0, 0), we can solve for S:
S = √(x₂² + y₂²) = √((0 - 1.9117)² + (0 - 0)²) ≈ 1.9117 AU
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