Velocity of a Hot-Air Balloon A hot-air balloon rises vertically from the ground so that its height after t sec is given by the following function.
h=1/2t2+1/2t
(a) What is the height of the balloon at the end of 40 sec?
(b) What is the average velocity of the balloon between t = 0 and t = 30?
ft/sec
(c) What is the velocity of the balloon at the end of 30 sec?
ft/sec

Answers

Answer 1

Answer:

Explanation:

Given the height reached by a balloon after t sec modeled by the equation

h=1/2t²+1/2t

a) To calculate the height of the balloon after 40 secs we will substitute t = 40 into the modeled equation and calculate the value of t

If h(t)=1/2t²+1/2t

h(40) = 1/2(40)²+1/2 (40)

h(40) = 1600/2 + 40/2

h(40) = 800 + 20

h(40) = 820 feet

The height of the balloon after 40 secs is 820 feet

b) Velocity is the change of displacement of a body with respect to time.

v = dh/dt

v(t) = 2(1/2)t²⁻¹ + 1/2

v(t) = t + 1/2

when v = 0sec

v(0) = 0 + 1/2

v(0) = 1/2 ft/sec

at v = 30secs

v(30) = 30 + 1/2

v(30) = 30 1/2 ft/sec

average velocity = v(30) - v(0)

average velocity = 30 1/2 - 1/2

average velocity of the balloon between t = 0 and t = 30 = 30 ft/sec

c) Velocity is the change of displacement of a body with respect to time.

v = dh/dt

v(t) = 2(1/2)t²⁻¹ + 1/2

v(t) = t + 1/2

The velocity of the balloon after 30secs will be;

v(30) = 30+1/2

v(30) = 30.5ft/sec

The velocity of the balloon after 30 secs is 30.5 feet/sec

Answer 2

A)  The height of the balloon at the end of 40 sec is 820 feet.

B) The average velocity of the balloon is 30 ft/sec.

C) The velocity of the balloon at the end of 30 sec is

Velocity

Given :

h=1/2t²+1/2t

Part A)

The height of the balloon after 40 secs is :

h(t)=1/2t²+1/2t

h(40) = 1/2(40)²+1/2 (40)

h(40) = 1600/2 + 40/2

h(40) = 800 + 20

h(40) = 820 feet

The height of the balloon after 40 secs is 820 feet

Part B)

The average velocity of the balloon is  :

v = dh/dt

v(t) = 2(1/2)t²⁻¹ + 1/2

v(t) = t + 1/2

when v = 0 sec

v(0) = 0 + 1/2

v(0) = 1/2 ft/sec

When at v = 30secs

v(30) = 30 + 1/2

v(30) = 30 1/2 ft/sec

average velocity = v(30) - v(0)

average velocity = 30 1/2 - 1/2

average velocity of the balloon = 30 ft/sec

The average velocity of the balloon  is  30 ft/sec.

Part C)

The velocity of the balloon at the end of 30 sec is :

v = dh/dt

v(t) = 2(1/2)t²⁻¹ + 1/2

v(t) = t + 1/2

The velocity of the balloon after 30secs will be;

v(30) = 30+1/2

v(30) = 30.5ft/sec

The velocity of the balloon after 30 secs is 30.5 feet/sec.

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Related Questions

In a polar coordinate system, the velocity vector can be written as . The term theta with dot on top is called _______________________ angular velocity transverse velocity radial velocity angular acceleration

Answers

Answer:

I believe it's called rapid growth

Explanation:

that is my answer no matter what

A rectangular block of metal of resistivity rho has dimensions d x 2d x 3d . A potential difference V is to be applied between two opposite faces of the block.
(A) To which two faces of the block should the potential difference be applied to give the maximum current density?
(B) What is the maximum current density j(subscript max) from part A?
(C) To which two faces of the block should the potential difference be applied to give the maximum current?
1. to the faces that area a distance d apart
2. to the faces that are a distance 2d apart
3. to the faces that are a distance 3d apart

Answers

Answer:

a) The potential difference should be applied to the d dimension face.

b) The maximum current density j = V/3ρd

c) 3. to the faces that are a distance 3d apart

Explanation:

a) Current density is the ratio of current flowing through a conductor, and cross-sectional area of the conductor. mathematically, it is written as

j = I/A

where I is the electric current, and

A is the area of the conductor.

From the equation, we can see that reducing the area of the conductor will increase the current density for a given amount of current passing through the conductor. The face d wide will give the least cross-sectional area of current flow.

b) current density can be gotten from

j = σE    ....equ 1

where σ is the conductivity of the conductor which is the inverse of resistivity ρ. this means that

σ = 1/ρ    ....equ 2

where ρ is the resistivity of the conductor

E is the electric field and is the volt through the conductor per unit length of the conductor

in this case, the maximum current density will be when the length is length 3d, and the volt is the potential difference V

therefore,

E = V/3d    ....equ 3

substituting equ 2 and equ 3 in equ1, we'll have

the maximum current density j = V/3ρd

c) To get the maximum current, the potential difference should be applied to the faces that are 3d wide apart because the resistance of a conductor varies inversely as the cross-sectional area. The maximum current will be gotten when the resistance is at its minimum, and the minimum resistance will be gotten with the most cross-sectional area. The 3d wide face will give the maximum cross-sectional area.

A helicopter blade starts to rotate from rest with a constant angular acceleration of \alpha=\:α = 0.98 radians/second2. How many revolutions will the blade make before it is rotating at 500 revolutions per minute (RPM)?

Answers

Answer:

n = 223 revolutions

Explanation:

It is given that,

The angular acceleration of a helicopter blade, [tex]\alpha =0.98\ rad/s^2[/tex]

Initial speed of the helicopter blade, [tex]\omega_i=0[/tex]

The final speed of the blade, [tex]\omega_f=500\ rpm=500\times \dfrac{2\pi}{60}\ rad/s=52.35\ rad/s[/tex]

We need to find the number of revolutions. Firstly we will find the angle turned by the blade. Let the angle is [tex]\theta[/tex]. So,

[tex]\omega_f^2-\omega_i^2=2\alpha \theta[/tex]

[tex]\theta=\dfrac{\omega_f^2}{2\alpha}[/tex]

[tex]\theta=1398.22\ rad [/tex]

Let there are n number of revolutions made by the blade. So,

[tex]n=\dfrac{\theta}{2\pi}\\\\n=\dfrac{1398.22}{2\pi}\\\\n=222.53\ rev[/tex]

or

n = 223 rev

So, there are 223 revolutions.

Sally who weighs 450 N, stands on a skate board while roger pushes it forward 13.0 m at constant velocity on a level straight street. He applies a constant 100 N force.


Work done on the skateboard


a. Rodger Work= 0J


b. Rodger work= 1300J


c. sally work= 1300J


d. sally work= 5850J


e. rodger work= 5850J

Answers

Answer:

b. Rodger work = 1300 J

Explanation:

Work done: This can be defined as the product of force and distance along the direction of the force.

From the question,

Work is done by Rodger using a force of 100 N  in pushing the skateboard through a distance of 13.0 m.

W = F×d............. Equation 1

Where W = work done, F = force, d = distance.

Given: F = 100 N, d = 13 m

Substitute these values into equation 1

W = 100(13)

W = 1300 J.

Hence the right option is b. Rodger work = 1300 J

A 800 kg safe is 2.1 m above a heavy-duty spring when the rope holding the safe breaks. The safe hits the spring and compresses it 46 cm. What is the spring constant of the spring?

Answers

Answer:

k = 17043.5 N/m = 17.04 KN/m

Explanation:

First we need to find the force applied by safe pn the spring:

F = Weight of Safe

F = mg

where,

F = Force Applied by the safe on the spring = ?

m = mass of safe = 800 kg

g = 9.8 m/s²

Therefore,

F = (800 kg)(9.8 m/s²)

F = 7840 N

Now, using Hooke's Law:

F = kΔx

where,

K = Spring Constant = ?

Δx = compression = 46 cm = 0.46 m

Therefore,

7840 N = k (0.46 m)

k = 7840 N/0.46 m

k = 17043.5 N/m = 17.04 KN/m

Suppose you are looking into the end of a long cylindrical tube in which there is a uniform magnetic field pointing away from you. If the magnitude of the field is decreasing with time the direction of the induced magnetic field is

Answers

Answer:

If the magnitude of the field is decreasing with time the direction of the induced magnetic field is CLOCKWISE

Explanation

This is because If the magnetic field decreases with time, the electric field will be produced in order to oppose the change in line with lenz law. Thus The right hand rule can be applied to find that the direction of electric field is in the clockwise direction.

You set two parallel slits 0.1 mm apart at a distance of 2 m from a screen and illuminate them with light of wavelength 450 nm. The distance between a bright spot in the interference pattern and the dark spot adjacent to it is Group of answer choices

Answers

Answer:

Δx = 9 x 10⁻³ m = 9 mm

Explanation:

The formula for fringe spacing in Young's Double Slit Experiment is given as follows:

Δx = λL/d

where,

Δx = fringe spacing = ?

λ = wavelength of light = 450 nm = 450 x 10⁻⁹ m

L = Distance between slits and screen = 2 m

d = distance between slits = 0.1 mm = 0.1 x 10⁻³ m

Therefore,

Δx = (450 x 10⁻⁹ m)(2 m)/(0.1 x 10⁻³ m)

Δx = 9 x 10⁻³ m = 9 mm

For every particle there is a corresponding ______________.

Answers

Answer:

Anti-Particle

A square coil of wire with side 8.0 cm and 50 turns sits in a uniform magnetic field that is perpendicular to the plane of the coil. The coil is pulled quickly out of the magnetic field in 0.2 s. If the resistance of the coil is 15 ohm and a current of 12 mA is induced in the coil, calculate the value of the magnetic field.

Answers

Answer:

Explanation:

area of the coil  A = .08 x .08 = 64 x 10⁻⁴ m ²

flux through the coil Φ = area of coil x no of turns x magnetic field

= 64 x 10⁻⁴ x 50 x B where B is magnetic field

emf induced = dΦ / dt = ( 64 x 10⁻⁴ x 50 x B - 0 ) / .2

= 1.6 B

current induced = emf induced / resistance

12 x 10⁻³ = 1.6 B / 15

B = 112.5 x 10⁻³ T .

Help me with these question and please explainnn

Answers

Explanation:

1.  Impulse = change in momentum

J = Δp

J = mΔv

In the x direction:

Jₓ = mΔvₓ

Jₓ = (0.40 kg) (30 m/s cos 45° − (-20 m/s))

Jₓ = 16.5 kg m/s

In the y direction:

Jᵧ = mΔvᵧ

Jᵧ = (0.40 kg) (30 m/s sin 45° − 0 m/s)

Jᵧ = 8.49 kg m/s

The magnitude of the impulse is:

J = √(Jₓ² + Jᵧ²)

J = 18.5 kg m/s

The average force is:

FΔt = J

F = J/Δt

F = 1850 N

2. Momentum is conserved.

m₁u₁ + m₂u₂ = (m₁ + m₂) v

In the x direction:

(1000 kg) (0 m/s) + (1500 kg) (-12 m/s) = (1000 kg + 1500 kg) vₓ

vₓ = -7.2 m/s

In the y direction:

(1000 kg) (20 m/s) + (1500 kg) (0 m/s) = (1000 kg + 1500 kg) vᵧ

vᵧ = 8 m/s

The magnitude of the final speed is:

v = √(vₓ² + vᵧ²)

v = 10.8 m/s

3. Momentum is conserved.

m₁u₁ + m₂u₂ = (m₁ + m₂) v

In the x direction:

(0.8 kg) (18 m/s cos 45°) + (0.36 kg) (9.0 m/s) = (0.8 kg + 0.36 kg) vₓ

vₓ = 11.6 m/s

In the y direction:

(0.8 kg) (-18 m/s sin 45°) + (0.36 kg) (0 m/s) = (0.8 kg + 0.36 kg) vᵧ

vᵧ = -8.78 m/s

The magnitude of the final speed is:

v = √(vₓ² + vᵧ²)

v = 14.5 m/s

The unit of current, the ampere, is defined in terms of the force between currents. Two 1.0-meter-long sections of very long wires a distance 1.5 m apart each carry a current of 1.0 A.

Required:
What is the force between them

Answers

Answer:

[tex]1.33\times 10^{-8} N[/tex]

Explanation:

According to the given scenario, the computation of force between them is shown below:-

As we know that

[tex]\mu = 4\pi\times 10^{-7}[/tex]

The force between two current carrying wires will be

[tex]F = \frac{\mu_oI_1I_2L}{2\pi r}[/tex]

[tex]= \frac{4\pi\times 10^{-7} (1 A) (1 A) (1.0 m)}{2\pi (1.5m)}[/tex]

[tex]= 1.33\times 10^{-7} N[/tex]

[tex]= 1.33\times 10^{-8} N[/tex]

Therefore for computing the force between two wires we simply applied the above formula.

So, the force between two wires carrying 1 A current [tex]= 1.33\times 10^{-8} N[/tex].

An unknown additional charge q3q3q_3 is now placed at point B, located at coordinates (0 mm, 15.0 mm ). Find the magnitude and sign of q3q3q_3 needed to make the total electric field at point A equal to zero.

Answers

Answer:

0.3nanocouloumb

Explanation:

Pls see attached file

a uniform rod of 30cm is pivoted at its center.a 40N weight is hung 5cm from left.from where 50N weight be hung to maintain equilibrium?

Answers

Answer:

The 50N weight be hung  at 23 cm to maintain equilibrium

Explanation:

Given;

length of the uniform rod = 30 cm

center of the uniform rod = 15 cm

weight of 40N is hung at 5 cm mark

weight of 50 N will be hung at ?

     0------5cm-----------------15cm-------------P---------30cm

              ↓             10cm      Δ       xcm    ↓

             40N                                             50N

Take moment about the pivot point and apply the principle of moment

50N (x cm) = 40N (10 cm)

x = (400) / 50

x = 8cm

P = x cm + 15 cm

P = 8 cm + 15 cm

P = 23 cm

Therefore, the 50N weight be hung  at 23 cm to maintain equilibrium

Suppose a small metal object, initially at a temperature of 40 degrees, is immersed in a room which is held at the constant temperature of 70 degrees. It takes 2 minutes for the temperature of the object to reach 55 degrees.

Required:
a. Calculate the heat transfer coefficient r , i.e. the constant of proportionality in the differential equation that describes Newton's law of cooling.
r =_________

b. Suppose now that the room temperature begins to vary; i.e. Troom(t) = 90 + sin(0.1 t) . Use Newton's law of cooling and the heat transfer coefficient you calculated in the previous step to compute the temperature of the object as a function of time. Suppose that T(0) = 70 . T(t)

Answers

a)The heat transfer coefficient  will be 0.231 .The concept of the Newtons law of cooling is used in the given problem.

What is newtons law of colling?

The pace at which an item cools is proportional to the temperature differential between the object and its surroundings,

According to Newton's law of cooling. Simply explained, in a cold environment, a glass of hot water will cool down faster than in a hot room.

The given data in the problem is;

T₀ is the initial temperature= 40°

[tex]\rm T_S[/tex]  is the constant temperature = 70°

T is the final temperature = 55°

From the given equation the Newtons law of cooling;

[tex]\rm T=T_S+(T_0-T_S)e^{-kt} \\\\ 55=70+(40-70)e^{-3k} \\\\-30 e^{-3k}=-15\\\\ e^{-3k}= -\frac{1}{2} \\\\ ln e^[3k}=ln 2 \\\\ K=\frac{1}{3} ln2 \\\\ K=0.231[/tex]

Hence the heat transfer coefficient  will be 0.231 .

To learn more about the Newtons law of cooling refer to the link;

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Chameleons catch insects with their tongues, which they can rapidly extend to great lengths. In a typical strike, the chameleon's tongue accelerates at a remarkable 210 m/s^2 for 20 ms, then travels at constant speed for another 30 ms.
During this total time of 50 ms, 1/20 of a second, how far does the tongue reach?
Express your answer to two significant figures and include the appropriate units.

Answers

Answer:

  x_total = 0.17m

Explanation:

We can treat this exercise with the kinematics equations, where in the first part it is accelerated and in the second it is a uniform movement.

Let's analyze accelerated motion

The time that lasts is t = 20 10⁻³ s, the initial speed is zero (v₀ = 0), let's find the length that advances

            x₁ = v₀ t + ½ a t²

            x₁ = ½ a t²

            x₁ = ½ 210 (20 10⁻³)²

            x₁ = 4.2 10⁻² m

 

let's find the speed for the end of this movement

            v = v₀ + a t

            v = 0 + 210   20 10⁻³

            v = 4.2 m / s

with this speed we can find the distance that the uniform movement

           x₂ = v t2

           x₂ = 4.2   30 10⁻³

           x₂ = 1.26 10⁻¹ m

           x₂ = 0.126m

the total distance traveled is

          x_total = x₁ + x₂

          x_total = 0.0420 +0.126

          x_total = 0.168m

           

     Let's reduce the significant figures to two

          x_total = 0.17m

Charge of uniform density (40 pC/m2) is distributed on a spherical surface (radius = 1.0 cm), and a second concentric spherical surface (radius = 3.0 cm) carries a uniform charge density of 60 pC/m2. What is the magnitude of the electric field at a point 4.0 cm from the center of the two surfaces?

Answers

Answer:

4.1 N/C

Explanation:

First of all, we know from maths that the surface area of a sphere = 4πr²

Charge on inner sphere ..

Q(i) = 40.0*10^-12C/m² x 4π(0.01m)²

Q(i) = 5.03*10^-14 C

Charge on outer sphere

Q(o) = 60*10^-12 x 4π(0.03m)²

Q(o) = 6.79*10^-13 C

Inner sphere has a - 5.03*10^-14C charge (-Qi) on inside of the outer shell. As a result, there is a net zero charge within the outer shell.

For the outer shell to show a NET charge +6.79*10^-13C, it's must have a +ve charge

= +6.79*10^-13C + (+5.03*10^-14C)

= +7.29*10^-13 C

Now again, we have

E = kQ /r²

E = (9.0*10^9)(+7.29*10^-13 C) / (0.04)²

E = 6.561*10^-3 / 1.6*10^-3

E = 4.10 N/C

Thus, the magnitude of the electric field is 4.1 N/C

"Pipe A has length L and is open at one end and closed at the other. Pipe B is open at both ends and has length 2L. Which harmonic of pipe B matches in frequency the fundamental of pipe A?"

Answers

Answer:

Explanation:

length of pipe A is L

frequency of fundamental note of pipe A which is closed organ pipe

= velocity of sound / 4 x length of pipe

=  V / 4 x L where V is velocity of sound .

Similarly frequency of fundamental note of pipe B which is open organ pipe

= velocity of sound / 2 x length of pipe

= V / (2 x 2L) =  V / 4L , This is also called first harmonic

so fundamental frequency of pipe A will be equal to first harmonic of pipe B .

why was the observation of the double-slit interference pattern more convincing evidence for the wave theory of light than the observation of diffraction

Answers

Answer:

The double slit experiment showed for the first time that light can be interfered, producing bands of light and dark fringes on a screen. This phenomenon was a unique and typical characteristic of waves.

Explanation:

Th double slit experiment by Thomas Young proved, and sealed for the first time the wave nature of light; showing that light just as any other wave can produce interference which was a unique, typical phenomenon of waves. The Interference of light was shown by allowing light to pass through narrow slits and superimpose on a wall or screen, at a distance away from the slit, producing a clear pattern of light and dark fringes. This was the first experiment to proof that darkness can be produced by the addition of light on light. Interference is accompanied by a spatial redistribution of the optical intensity without violation of power conservation. The phenomenon of interference proved the intuitive ideas of Huygens regarding the wave nature of light against Newton's particle nature of light theory.

A skater spins at 3rev/s when she stretches her arms outward. If she keeps her fists on her chest she can spin at 4.5rev/s and her body inertia is 3kg.m2. What is her body inertia when she stretches her arms outward?

Answers

Answer:

Body inertia I = 4.5 kg/m^2

Explanation:

Here, we want to calculate the body inertia when the arms are stretched outwards.

We know from the question that angular momentum is conserved

Thus;

I * 3 = 4.5 * 3

I = 4.5 kg/m^2

Red light is bent the least of all colors as it passes through a prism. What does this tell you about red light? It has a short wavelength. It has a long wavelength. It has a high intensity. It has a low intensity.

Answers

Answer:

Longest wavelength, lowest intensity

Explanation:

Answer:

It has a long wavelength

Explanation:

GRADPOINT

Often in science it is helpful to talk about a representative example of the objects or phenomena being studied. However, you must always keep in mind that the average case is not always representative. For example, our Sun is often described as an "average" star in the Milky Way. In what sense is this statement true? In what sense is this statement seriously misleading? Do you think it is useful to characterize the stars in the Milky Way by simply citing our "average" Sun?

Answers

Explanation:

The statement "our sun is an 'average' sun" is  true when it is used to describe or characterize some unique physical properties of stars generally in the universe. 'Average' in this sense is used to define a typical sun such as, "stars should glow like our sun an average star."

The statement is used wrongly when used to in quantifying other stars in the universe, based on calculated values from our sun. In this case, we cannot truly say if our sun is a true representative average of other stars in the universe.

Yes! it is useful to characterize the milky way by simply citing the average sun. Properties like their ability to glow and radiate heat can be defined by citing an average star like our sun, so long as we don't translate it into citing quantitative properties of the sun as an average of our Milky Way Galaxy like the mass, temperature, etc.

An inventor claims to have developed a food freezer that, in steady-state conditions, requires a power input of 0.25 kW to extract energy by heat transfer at a rate of 3050 J/s from the freezer contents, which are at a temperature of 270 K. Determine if this claim is real considering an ambient temperature of 293 K. (a) Can the freezer operation in such conditions

Answers

Answer:

The inventors  claim is not real

a)  No the the freezer cannot operate in such conditions

Explanation:

From the question we are told that

     The  power input is  [tex]P_i = 0.25 kW = 0.25 *10^{3} \ W[/tex]

      The  rate of heat transfer [tex]J = 3050 J/s[/tex]

       The temperature of the freezer content is [tex]T = 270 \ K[/tex]

       The  ambient temperature is  [tex]T_a = 293 \ K[/tex]

Generally the coefficient of performance of a refrigerator at idea conditions is mathematically represented as

      [tex]COP = \frac{T }{Ta - T}[/tex]

substituting values

     [tex]COP = \frac{270 }{293 - 270}[/tex]

     [tex]COP =11.7[/tex]

Generally the coefficient of performance of a refrigerator at real conditions is mathematically represented as

       [tex]COP = \frac{J}{P_i}[/tex]

substituting values

       [tex]COP = \frac{3050}{0.25 *10^{3}}[/tex]

       [tex]COP = 12.2[/tex]

Now given that the COP  of an ideal refrigerator is  less that that of a real refrigerator then the claims of the inventor is rejected

This is because the there are loss in the real refrigerator cycle that are suppose to reduce the COP compared to an ideal refrigerator cycle where there no loss that will reduce the COP

A proton moving at 4.80 106 m/s through a magnetic field of magnitude 1.74 T experiences a magnetic force of magnitude 7.00 10-13 N. What is the angle between the proton's velocity and the field? (Enter both possible answers from smallest to largest. Enter only positive values between 0 and 360.)

Answers

Answer:

31.55° and 148.45°

Explanation:

Formula for calculating the force experiences by the proton placed in a magnetic field is as expressed below;

F = qvBsinθ where;

F is the magnetic force experienced by the proton

q is the charge on the proton

v is the velocity of the proton

B is the magnetic field

θ is the angle between the proton's velocity and the field (Required)

Given parameters

F =  7.00 * 10⁻¹³N

q = 1.602*10⁻¹⁹C

v = 4.80 * 10⁶ m/s

B = 1.74 T

θ  =?

From the formula F = qvBsinθ;

sinθ = F/qvB

sinθ = 7.00 * 10⁻¹³/1.602*10⁻¹⁹* 4.80 * 10⁶*1.74

sinθ =  7.00 * 10⁻¹³/13.38*10⁻¹³

sinθ = 0.5231689 * 10⁰

sinθ = 0.5231689

θ = sin⁻¹0.5231689

θ = 31.55°

The following are the positive values of the angle between 0° and 360°

Sin is positive in the first and second quadrant. In the second quadrant the angle is equal to 180°-31.55° = 148.45°.

Hence the possible values of the angle from smallest to largest are 31.55° and 148.45°

The refractive index n of transparent acrylic plastic (full name Poly(methyl methacrylate)) depends on the color (wavelength) of the light passing through it. At wavelength 486.1 nm (blue, designated with letter F) -> nF=1.497, and at wavelength 656.3 nm (red, designated with letter C) -> nC=1.488. Two beams (one of each wavelength) are prepared to coincide, and enter the flat polished surface of an acrylic block at angle of 45 arc degree measured from the normal to the surface. What is the angle between the blue beam and the red beam in the acrylic block?

Answers

Answer:

The angle between the blue beam and the red beam in the acrylic block is  

 [tex]\theta _d =0.19 ^o[/tex]

Explanation:

From the question we are told that

     The  refractive index of the transparent acrylic plastic for blue light is  [tex]n_F = 1.497[/tex]

     The  wavelength of the blue light is [tex]F = 486.1 nm = 486.1 *10^{-9} \ m[/tex]

    The  refractive index of the transparent acrylic plastic for red light is  [tex]n_C = 1.488[/tex]

       The  wavelength of the red light is [tex]C = 656.3 nm = 656.3 *10^{-9} \ m[/tex]

    The incidence angle is  [tex]i = 45^o[/tex]

Generally from Snell's law the angle of refraction of the blue light  in the acrylic block  is mathematically represented as

       [tex]r_F = sin ^{-1}[\frac{sin(i) * n_a }{n_F} ][/tex]

Where  [tex]n_a[/tex] is the refractive index of air which have a value of[tex]n_a = 1[/tex]

So

     [tex]r_F = sin ^{-1}[\frac{sin(45) * 1 }{ 1.497} ][/tex]

      [tex]r_F = 28.18^o[/tex]

Generally from Snell's law the angle of refraction of the red light in the acrylic block is mathematically represented as

       [tex]r_C = sin ^{-1}[\frac{sin(i) * n_a }{n_C} ][/tex]

Where  [tex]n_a[/tex] is the refractive index of air which have a value of[tex]n_a = 1[/tex]

So

     [tex]r_C = sin ^{-1}[\frac{sin(45) * 1 }{ 1.488} ][/tex]

      [tex]r_F = 28.37^o[/tex]

The angle between the blue beam and the red beam in the acrylic block

     [tex]\theta _d = r_C - r_F[/tex]

substituting values

       [tex]\theta _d = 28.37 - 28.18[/tex]

       [tex]\theta _d =0.19 ^o[/tex]

 

A car is moving along a road at 28.0 m/s with an engine that exerts a force of
2,300.0 N on the car to balance the drag and friction so that the car maintains a
constant speed. What is the power output of the engine?

Answers

Answer:

Power = Force × Distance/time

Power = Force × Velocity

Power = 2,300.0 N × 28.0 m/s²

Power = 64400 Nm/s

Explanation:

First show the formula of Power

Re-arrange formula and used to work out Power

Pretty simple stuff!

Hope this Helps!!

g A particle (charge = +40 mC) is located on the x axis at the point x = -20 cm, and a second particle (charge = -50 mC) is placed on the x axis at x = +30 cm. What is the magnitude of the total electrostatic force on a third particle (charge = -4.0 mC) placed at the origin (x = 0)? Group of answer choices

Answers

Answer:

Explanation:

We shall find electric field at origin due to two given charges sitting   on the either side of origin .

Total field will add up due to their same direction .

Field due to a charge Q

= 9 x 10⁹ x Q / R²  ;  R is distance of point , Q is charge

Field due to first charge

= 9 x 10⁹ x 40 x 10⁻³ / 2² x 10⁻⁴

= 90 x 10¹⁰ N/C

Field due to second  charge

= 9 x 10⁹ x 50 x 10⁻³ / 2² x 10⁻⁴

= 112.5 x 10¹⁰ N/C

Total field

= 202.5 x 10¹⁰ N/C

Force on given charge at origin

= charge x field

= 4 x 10⁻³ x 202.5 x 10¹⁰

= 810 x 10⁷ N .

The 2-Mg truck is traveling at 15 m/s when the brakes on all its wheels are applied, causing it to skid for 10 m before coming to rest. The total mass of the boat and trailer is 1 Mg. Determine the constant horizontal force developed in the coupling C, and the friction force developed between the tires of the truck and the road during this time.

Answers

Answer:

constant horizontal force developed in the coupling C = 11.25KN

the friction force developed between the tires of the truck and the road during this time is 33.75KN

Explanation:

See attached file

The friction force between the tires of the truck and the road is 22500 N.

Calculating the friction force:

It is given that a 2 Mg truck ( m = 2000 Kg) is initially moving with a speed of u = 15 m/s.

Distance traveled before coming to rest, s = 10m

The final velocity of the truck will be zero, v = 0

When the breaks are applied, only the frictional force is acting on the truck and it is opposite to the motion of the truck.

The frictional force is given by:

f = -ma

the acceleration of the truck = -a

The negative sign indicates that the acceleration is opposite to the motion.

Applying the third equation of motion we get:

v² = u² -2as

0 = 15² - 2×a×10

225 = 20a

a = 11.25 m/s²

So the magnitude of frictional force is:

f = ma = 2000 × 11.25 N

f = 22500 N

Learn more about friction force:

https://brainly.com/question/1714663?referrer=searchResults

A skateboarder jumps horizontally off the top of a staircase and lands at bottom of the stairs. The staircase has a horizontal length of 12.0 m, and the jump lasts 1.10s. We can ignore air resistance. What is the skater's vertical velocity upon landing? Round your answer to three significant digits.

Answers

Answer:

The vertical velocity of the skater upon landing is 10.788 meters per second.

Explanation:

Skateboarder experiments a parabolic movement. As skateboarder jumps horizontally off the top of the staircase, it means that vertical component of initial velocity is zero and accelerates by gravity, the final vertical speed is calculated by the following expression:

[tex]v = v_{o} + g\cdot t[/tex]

Where:

[tex]v_{o}[/tex] - Initial vertical speed, measured in meters per second.

[tex]v[/tex] - Final vertical speed, measured in meters per second.

[tex]g[/tex] - Gravitational acceleration, measured in meters per square second.

[tex]t[/tex] - Time, measured in seconds.

Given that [tex]v_{o} = 0\,\frac{m}{s}[/tex], [tex]g = -9.807\,\frac{m}{s^{2}}[/tex] and [tex]t = 1.10\,s[/tex], the final velocity of the skater upon landing is:

[tex]v = 0\,\frac{m}{s} + \left(-9.807\,\frac{m}{s^{2}} \right)\cdot (1.10\,s)[/tex]

[tex]v = -10.788\,\frac{m}{s}[/tex]

The vertical velocity of the skater upon landing is 10.788 meters per second.

Answer:

-10.8

Explanation:

Answer on Khan Academy

n oscillator is driven by a sinusoidal force. The frequency of the applied force A : must be less than the natural frequency of the oscillator. B : is independent of the natural frequency of the oscillator. C : becomes the natural frequency of the oscillator. D : must be equal to the natural frequency of the oscillator. E : must be greater than the natural frequency of the oscillator

Answers

Answer:

  B : is independent of the natural frequency of the oscillator

Explanation:

You can apply any force you like to a natural oscillator. It is independent of the natural frequency of the oscillator.

The result you get will depend on how the frequency of the applied force and the natural frequency relate to each other. It will also depend on the robustness of the oscillator with respect to the applied force.

Clearly, if the force is small enough, it will have no effect on the oscillator. If it is large enough, it will overpower any motion the oscillator may attempt. For forces in the intermediate range, there will be some mix of natural oscillation and forced behavior. One may modulate the other, for example.

A person can survive a feet-first impact at a speed of about 12 m/s (27 mi/h) on concrete, 15 m/s (34 mi/h) on soil, and 34 m/s (76 mi/h) on water. What is the reason for the different values for different surfaces

Answers

Answer:

Different surfaces have different impact force during collision which depends on the time it takes the person to come to rest after collision.

Explanation:

Given;

speed on concrete = 12 m/s (27 mi/h)

speed on soil = 15 m/s (34 mi/h)

speed on water = 34 m/s (76 mi/h)

The impact force on this person during collision is rate of change of momentum;

[tex]F = \frac{\delta P}{\delta t}[/tex]

During collision, the force exerted on this person depends on how long the collision lasts; that is, how long it takes for this person to come to rest after collision with each of the surfaces.

The longer the time of collision, the smaller the force exerted by each.

It takes shorter time for the person to come to rest on concrete surface than on soil surface, also it takes shorter time for the person to come to rest on soil surface than on water surface.

As a result of the reason above, the force exerted on the person during collision by the concrete surface is greater than that of soil surface which is  greater than that of water surface.

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