As light shines from air to water, the index of refraction is 1.02 and the angle of incidence is 38.0 °. What is the light's angle of refraction?

39.8°
37.1°
29.8°
32.5°

Solution :

From the Newton's second law of motion :

F = ma

[tex]a=\frac{F}{m}[/tex]

[tex]$\frac{dv}{dt}=\frac{F}{m}$[/tex]

[tex]$\left(\frac{dv}{ds} \times \frac{ds}{dt}\right)=\frac{F}{m}$[/tex]

[tex]$v \frac{dv}{ds} = \frac{F}{m}$[/tex]

[tex]$v dv =\frac{F}{m}\ ds$[/tex]

Integrating above the expression by applying the limits :

[tex]$\int_{v_i}^{v_f} v \ dv= \frac{F}{m} \int_0^s ds$[/tex]

Here the diameter is s= D

[tex]$\frac{v_f^2 - v_i^2}{2}=\frac{FD}{m}$[/tex]

The final speed of the particle after travelling distance D is

[tex]$v_f = \sqrt{v_i^2 + \frac{2FD}{m}}$[/tex]

The kinetic energy of the particle of mass M is :

[tex]$K_1=\frac{1}{2}Mv^2$[/tex]

For M = 3M

[tex]$K_2=\frac{1}{2}(3M)v^2$[/tex]

     [tex]$=3(K_1)$[/tex]

Thus the kinetic energy increases by a factor of 3.

The work done depends on the factor and the displacement of the body. Thus, the work done remains same even though the mass increases. Hence the work down increases by factor 1.

Answer: [tex]1.23\ m/s^2[/tex]

Explanation:

Given

At an elevation of [tex]y=34.7\ km[/tex], spacecraft is dropping vertically at a speed of [tex]u=293\ m/s[/tex]

Final velocity of the spacecraft is [tex]v=0[/tex]

using equation of motion i.e. [tex]v^2-u^2=2as[/tex]

Insert the values

[tex]\Rightarrow 0-(293)^2=2\times a\times (34.7\times 10^3)\\\\\Rightarrow a=-\dfrac{293^2}{2\times 34.7\times 10^3}\\\\\Rightarrow a=-1.23\ m/s^2[/tex]

Therefore, magnitude of acceleration is [tex]1.23\ m/s^2[/tex].

Answer:

D)378kJ

Explanation:

Applying,

E = F×d................ Equation 1

Where E = Energy expanded by the car, F = Wind resistance, d = distance

From the question,

F = 0.42v²............ Equation 2

Susbtitute equation 2 into equation 1

E = 0.42v²d.............. Equation 3

Given: v = 30 m/s, d = 1 km = 1000 m

Substitute these values into equation 3

E = 0.42(30²)(1000)

E = 378000

E = 378 kJ

Hence the right option is D)378kJ

Explanation:

A nichrome (ρ = 100x10-8 Ωm) wire has a diameter of 0.40 mm. ... A power line with a resistance of 2 ohms has a current of 80 A in it

1/8 Watt 50 kΩ resistor has 70 V applied.

A 50 Ω resistor in a circuit has a current flowing through it of 2.0 A then the power dissipated by the resistor is 200 Watt. Therefore the correct option is B.

The rate of doing work is known as power. The Si unit of power is the watt.

Power =work/time

The mathematical expression for the power is as follows

P = VI

where P is the power

V is the voltage

I is  current passing through the circuit

The expression of power can be represented in many different forms by using the ohms law

As we know from Ohm's law that V= IR

Power = VI

by substituting V=IR in place of the voltage in power formula

P = I²R

As given in the problem a 50 Ω resistor in a circuit has a current flowing through it of 2.0 A so by substituting the values of the current and the resistance in the formula of power

P = 2²×50

  = 200 Watt

Therefore the correct answer is B.

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Answer:

219 m/s

Explanation:

Kinetic energy is calculated using the formula:

Given:

We can solve for the unknown variable v.

Substitute these known values into the formula.

The velocity of the car is around 219 m/s.

Answer:

[tex]B_2=2.1nT[/tex]

Explanation:

From the question we are told that:

Frequency [tex]F=800kHz[/tex]

Distance [tex]d=4.5km[/tex]

Electric field amplitude [tex]B_2=0.63V/m[/tex]

Generally the equation for momentum is mathematically given by

 [tex]B=\frac{E}{C}[/tex]

Therefore

 [tex]B_2=\frac{0.63}{3*10^8}[/tex]

 [tex]B_2=0.21*10^{-8}[/tex]

 [tex]B_2=2.1nT[/tex]

Answer:

The minute hand travels 2π radians in 60 minutes , so the angular velocity is

[tex]angular \: velocity = \frac{2\pi \: radians}{60m} \\ = \frac{\pi}{30} radians \: per \: min[/tex]

The angular velocity of the minute arm will be [tex]\frac{\pi }{30}[/tex]  rad/second.

We have the minute arm of the clock that completes one complete revolution in 60 seconds.

We have to determine its angular velocity.

The formula to calculate the angular velocity of body is as follows -

ω = [tex]\frac{d\theta}{dt}[/tex] = [tex]\frac{\theta_{2} -\theta_{1} }{t_{2} -t_{1} }[/tex]

According to the question -

For one complete revolution -   [tex]\theta_{2} -\theta_{1} =[/tex] 2[tex]\pi[/tex] - 0 = 2[tex]\pi[/tex].

and

[tex]t_{2} -t_{1}[/tex] = 60 - 0 = 60 seconds.

Therefore, the angular velocity of the minute arm of the clock will be -

ω = [tex]\frac{2\pi }{60}[/tex] = [tex]\frac{\pi }{30}[/tex] rad/second

Hence, the angular velocity of the minute arm will be [tex]\frac{\pi }{30}[/tex]  rad/second.

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Answer:

Option (b) is correct.

Explanation:

An object travels down a ramp at a constant acceleration.

Friction force and the gravitational force is there.

(a). It is false. As the friction acts in the opposite direction of motion of the object.

(b). It is true. As the object moves down the ramp so the force of friction is less the component of gravitational force along the ramp.

(c). It is false. the acceleration does not depends on the mass.

a = g sin A - u g cos A

where, A is the angle of inclination and u is the coefficient of friction.

(d). It is false. The normal force is given by

N = m g cos A

so it depends on the mass.

Answer:

the sound intensity at the position of the microphone is 7.4 × 10⁻⁴ W/m²

Explanation:

Given the data in the question;

Sound power P = 26.0 W

Area of microphone A = 1.00 cm²

Radius r = 53.0 m

sound intensity at the position of the microphone = ?

Now, intensity at the position of the microphone can be determined using the following expression;

[tex]I[/tex] = P / 4πr²

We substitute

[tex]I[/tex] = 26.0 / ( 4 × π × (53.0 )² )

[tex]I[/tex] = 26.0 / ( 4 × π × 2809 )

[tex]I[/tex] = 26.0 / 35298.935

[tex]I[/tex] = 26.0 / ( 4 × π × (53.0 )² )

[tex]I[/tex] = 0.000736566

[tex]I[/tex] = 7.4 × 10⁻⁴ W/m²

Therefore, the sound intensity at the position of the microphone is 7.4 × 10⁻⁴ W/m²

Answer:im just guessing d but i think its d though

Explanation:

it pretty obvious

Answer:

ON

Explanation:

Locate your computer's Power button.

Press and hold that button until your computer shuts down.

Wait until you hear the computer's fans shut off, and your screen goes completely black.

Wait a few seconds before pressing and holding the power button to initiate your computer's normal startup.

Answer:

50 km/h

Explanation:

From the graph, we can deduce the following parameters;

Distance = 20, 40, 60, 80, 100 km

Time = 0.5, 1.0, 1.5, 2.0 hours

To find the average velocity of the car over the first 2.00 hours.

First of all, we would determine the total distance and time.

Total distance = 20 + 40 + 60 + 80 + 100 = 300 km

Total time = 0.5 + 1.0 + 1.5 + 2.0 = 5

Average velocity = distance/time

Average velocity = 100/2

Average velocity = 50 km/h

Answer:

Hello There!!

Explanation:

The answer is O parallel.

hope this helps,have a great day!!

~Pinky~

Answer:

From 0.75 to 1.25 hours

Explanation:

Given

See attachment for graph

Required

Point where they didn't move

This means that we identify the point where the distance didn't change.

Given that the distance is plotted on the y-axis, we simply check for the end points of any horizontal line on the graph

The horizontal line on the graph represents 30km and the time interval is: 0.75 to 1.25 hours.

Hence, (c)  is correct

Answer:

Here's an explanation but not the answer

Explanation:

When a resistor is traversed in the same direction as the current, the ... Traversing the internal resistance r1 from c to d gives −I2r1. ... I1 = I2 + I3 = (6−2I1) + (22.5− 3I1) = 28.5 − 5I1.

Answer:

Acceleration is the rate of change in velocity. Momentum is the mass times the velocity. So if you multiply the mass times the acceleration, you get the of change of momentum.

Answer:

1/2 m v^2 = m g H      conservation of energy

H = (v^2 / (2 * g))^1/2 = (14^2 / 19.6)^1/2 = 10 m

H = 1/2 g t^2       time to fall 10 m

t = (2 * H / g)^1/2 = (20 / 9.8)^1/2 = 1.43 sec

Total time in air = 2 * 1.43 = 2.86

You can also use 2 a S = V0^2 since final velocity = 1.43 * 9.8 m/s = 14 m / s

and 2 a S = 2 * 9.8 * 10 = 196 m^2 / s^2   which is V0 squared

Answer:

g m t o k liye cbbhhhf to be be free and ear is not a short time to be a short of a week and I am a short kat key and ear to be free and ear is not a short time and ear buds and duster for a short of a week of the action is not by the action is not a short time to make sure to be free and duster and not by the way to

Explanation:

ahhhhhhh to be be free and ear is nothing to be be free and ear is not a short time to be be free and ear is not by the class is not a a short time to be be free and

Answer:

I HOPE THIS IS CORRECT

Explanation:

It is heated from 20°C to 80°C. We need to find the heat absorbed. It can be given by the formula as follows : So, 1386 J of heat is absorbed.

Given :

Initial velocity , u = 0 m/s² .

To Find :

The acceleration of the cart.

Solution :

Since, acceleration is constant.

Using equation of motion :

[tex]x = ut + \dfrac{at^2}{2}\\\\x = \dfrac{at^2}{2}[/tex]

Putting, t = 1 s  and x = 4 m in above equation, we get :

[tex]4 = \dfrac{a(1)^2}{2}\\\\a = 8 \ m/s^2[/tex]

Therefore, the acceleration of the cart is 8 m/s².

Answer:

a) P = 70054.3 W,  b)  P = 18820 W,  c)   P = 14116.7 W

Explanation:

Power is defined as work per unit of time

         P = W / t = F x / t

         P = F v

a) in this case the velocity is constant, let's use the equilibrium relation to find the force.

Let's set a reference system with the x axis parallel to the plane

        F - Wₓ = 0

         F = Wₓ

with trigonometry let's decompose the weight

        sin θ = Wₓ / W

        Wₓ = W sin θ

          F = W sin 15

          F = 2800 sin 15

          F = 724.7 lb

we look for the speed, as it rises with constant speed we can use the relations of uniform motion

          v = x / t

          v = 1160/12

          v = 96.67 ft / s

we calculate the power

          P = 724.7 96.67

          P = 70054.3 W

b) In this case, the speed of the vehicle changes during the ascent, so we use the relationship between work and the change in kinetic energy

           W = ΔK

           W = ½ m v_f² - ½ m v₀²

   let's reduce to the SI system

           v₀ = 10 mph (5280 ft / 1 mile) (1h / 3600 s = 14.67 ft / s

           v_f = 50 mph (5280 ft / 1 mile) (1 h / 3600s) = 73.33 ft.s

 mass :         m = w / g

           W = ½ 2800/32 (73.33² - 14.67²)

           W = 225841 J

we calculate the average power

           P = W / t

           P = 225841/12

           P = 18820 W

c) we repeat the previous procedure

          v₀ = 45 mph = 66 ft / s

          v_f = 15 mph = 22 ft / s

          W = ½ 2800/32 (22² - 66²)

          W = -169400 J

          P = W / t

          P = 169400/12

          P = 14116.7 W

Explanation:

hmm! very good questions I hope u understand

Answer:

Climate change means a change in the state of the climate system that is sustained over a long period of time. These types of changes can occur due to natural or human causes.

Climate change and its effects on the planet can generate massive migrations, given the affectation of nature in certain parts of the planet.

Thus, an example would be the migration of populations from island countries, such as Fiji, Tonga or Samoa, to continental territories, due to the rise in sea level caused by the melting of the poles due to global warming.

Another example may be the desertification of certain regions, which would encourage migration by the inhabitants of these places to other territories.

Finally, climate change and its negative effects not only generate massive migrations caused by natural effects, but also by the economic effects of said changes, that is, by increases in poverty and inequality in the face of the scarcity of certain natural resources.

Answer:

Appliance A and B can work together without tripping

Explanation:

We will calculate the amount of current consumed by each appliances.

Appliance A

P = VI

I = P/V  

I = 250/120 = 2.08 A

Appliance B

I = 480 /120 = 4 A

Appliance C

I = 1450/120

I = 12.08 A

Hence, appliance C will trip the circuit as it consumes a lot of electricity.

Answer:

the current through the circuit is 10 A.

Explanation:

Given;

voltage of the battery, V = 10 V

number of the parallel resistors, = 3

resistance of each resistor, r = 3 ohms

The equivalent resistance is calculated as;

[tex]\frac{1}{R_t} = \frac{1}{r_1}+ \frac{1}{r_2} + \frac{1}{r_3} \\\\\frac{1}{R_t} = \frac{1}{3}+ \frac{1}{3} + \frac{1}{3}\\\\\frac{1}{R_t} =\frac{3}{3} \\\\\frac{1}{R_t} = 1\\\\R_t = 1 \ ohms[/tex]

The current through the circuit is calculated as;

V = IRt

I = V/Rt

I = 10/1

I = 10 A

Therefore, the current through the circuit is 10 A.

Explanation:

Adaptations are any behavioral or physical characteristics of an animal that help it to survive in its environment

Answer:

Coefficient of friction is [tex]0.068[/tex].

Work done is [tex]320~J[/tex].

Explanation:

Given:

Mass of the box ([tex]m[/tex]): [tex]60[/tex] kg

Force needed ([tex]F[/tex]): [tex]40[/tex] N

The formula to calculate the coefficient of friction between the floor and the box is given by

[tex]F=\mu mg...................(1)[/tex]

Here, [tex]\mu[/tex] is the coefficient of friction and [tex]g[/tex] is the acceleration due to gravity.

Substitute [tex]40[/tex] N for [tex]F[/tex], [tex]60[/tex] kg for [tex]m[/tex] and [tex]9.80[/tex] m/s² for [tex]g[/tex] into equation (1) and solve to calculate the value of the coefficient of friction.

[tex]40 N=\mu\times60 kg\times9.80 m/s^{2} \\~~~~~\mu=\frac{40 N}{60 kg\times9.80 m/s^{2}}\\~~~~~~~=0.068[/tex]

The formula to calculate the work done in overcoming the friction is given by

[tex]W=Fd..........................(2)[/tex]

Here, [tex]W[/tex] is the work done and [tex]d[/tex] is the distance travelled.

Substitute  [tex]40[/tex] N for [tex]F[/tex] and [tex]8 m[/tex] for [tex]d[/tex] into equation (2) to calculate the work done.

[tex]W=40~N\times8~m\\~~~~= 320~J[/tex]

Answer:

 x₃ = 0.0725 m

Explanation:

The force between the particles is electrical

          F = [tex]k \frac{q_1q_2}{r_{12}^2}[/tex]

          F = q₀ E_total

don q₀ is a positive test charge at the point of interest, therefore we can calculate the electric field at the point of interest x₀ = 0.25 cm

          F = 0   → E_total = 0

          E_total = E₁ + E₂ + E₃

           E_total = [tex]k \frac{q_1}{r_{1o}^2} + k \frac{q_2}{r_{2o}^2} + k \frac{q_3}{r_{3o}^2}[/tex]

          E_total = k ( [tex]\frac{q_1}{r_{1o}^2} + \frac{q_2}{r_{2o}^2} + \frac{q_3}{r_{3o}^2}[/tex] )

let's look for the distances

          r₁₀ = (x₀ - 0)

          r₁₀ = 0.25 m

          r₂₀ = √(x₀ - x₂) ²

          r₂₀ = √ (0.25 - 0.15) ²

          r₂₀ = 0.10 m

          r₃₀ = √ (0.25 - x₃) ²

we substitute

           0 = 9 10⁹ (4 / 0.25² - 2.1 / 0.1² + 4.6 / (0.25-x₃)² )

            4.6 / (0.25-x3)² = -4 / 0.25² + 2.1 / 0.1²

             4.6 / (0.25-x3) ² = -146

             (0.25 - x3) ² = - 4.6 / 146 = - 0.0315068

              0.25 - x3 = 0.1775

              x₃ = 0.25 - 0.1775

              x₃ = 0.0725 m