g A proton travels through uniform magnetic and electric fields. The magnetic field is in the negative x direction and has a magnitude of 1.97 mT. At one instant the velocity of the proton is in the positive y direction and has a magnitude of 1680 m/s. At that instant, what is the magnitude of the net force acting on the proton if the electric field is (a) in the positive z direction and has a magnitude of 4.34 V/m, (b) in the negative z direction and has a magnitude of 4.34 V/m, and (c) in the positive x direction and has a magnitude of 4.34 V/m

Answer:

C

Explanation:

In order to obtain data about the object’s velocity as a function of time, the object must move either toward or away from the motion detector.

The student cannot determine the relationship using this experiment ; ( C ) Because the motion detector should be oriented so that the object moves parallel to the line along which the front of the motion detector is aimed

Given that the aim of the experiment is to determine the relationship between mass of inertia of object, net force exerted and acceleration of the object we have to first obtain the object's velocity (i.e. Distance travelled by object / time ). and

To obtain velocity of object with respect to time, the object must move in either direction ( back or front ) from its parallel position away from the position of the detector ( motion )

Hence we can conclude that The student cannot determine the relationship using this experimental procedures.Because the motion detector should be oriented so that the object moves parallel to the line along which the front of the motion detector is aimed

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Answer:

No

Explanation:

It was made in the 17th century

Answer:

Function

Explanation:

This question defines a function. It is any consequence that is made up of positive structures which has a way of affecting the society in a positive way. And it also has a way of impacting structural continuity in the society. The functionalism idea has the postulation that all cultural or social phenomena is of positive function and cannot be ignored

Answer:

function

Explanation:

answer EDGE2020

Answer:

Community A

Explanation:

Community A most likely use hydroelectric power for generating most of their electricity.

Hydroelectric power utilizes the energy from water to produce electricity.

A water body is dammed, then channeled for driving a turbine which in turn generates electricity by induction.

Answer:

(a)  24.56 N

(b) 142.28 N

Explanation:

(a)

The designation assigned to something like the net force pointed toward the middle including its circular route seems to be the centripetal force. The net stress only at lowest point constitutes of the strain throughout the arm projecting upward towards the middle as well as the weight pointed downwards either backwards from the center.

The centripetal function is generated from either scenario by Equation:

⇒  [tex]Fc = \frac{mv^2}{r}[/tex]

On putting the values, we get

⇒       [tex]=\frac{12\times 1.33^2}{0.864}[/tex]

⇒       [tex]=24.56 \ N[/tex]

(b)

Use T to denote whatever arm stress we can get at the bottom including its circle:

⇒  [tex]Fc = T - mg =\frac{ mv^2}{r}[/tex]

⇒  [tex]T = mg + Fc[/tex]

⇒      [tex]=12\times 9.81+24.56[/tex]

⇒      [tex]=142.28 \ N[/tex]

Answer:

I am confused of your question. Do you want final velocity? To get final velocity, use (initial V)+(Gravity*Time)

Explanation:

Answer:

B. g*t

Explanation:

Answer:

10 mls2

Explanation:

speed =distance /time

Answer:

D

Explanation:

Answer:

The answer is C. Strong Nuclear

Explanation:

I took this test and it was correct!

Answer:

58.32 N

Explanation:

Area of a circle = [tex]\pi[/tex][tex]r^{2}[/tex]

where r is the radius of the circle.

The cylinder has a radius of 0.02 m, its area is;

[tex]A_{1}[/tex] = [tex]\pi[/tex][tex]r^{2}[/tex]

  = [tex]\frac{22}{7}[/tex] x [tex](0.02)^{2}[/tex]

  = [tex]\frac{22}{7}[/tex] x 0.0004

  = 1.2571 x [tex]10^{-3}[/tex]

Area of the cylinder is 0.0013 [tex]m^{2}[/tex].

The safety valve has a radius of 0.0075 m, its area is;

[tex]A_{2}[/tex] = [tex]\pi[/tex][tex]r^{2}[/tex]

    = [tex]\frac{22}{7}[/tex] x [tex](0.0075)^{2}[/tex]

    = [tex]\frac{22}{7}[/tex] x 5.625 x [tex]10^{-5}[/tex]

    = 1.7679 x [tex]10^{-4}[/tex]

Area of the valve is 0.00018 [tex]m^{2}[/tex].

From Hooke's law, the force on the safety valve can be determined by;

F = ke

[tex]F_{2}[/tex]  = 950 x 0.0085

  = 8.075 N

Minimum force, [tex]F_{1}[/tex], required can be determined by;

[tex]\frac{F_{1} }{A_{1} }[/tex] = [tex]\frac{F_{2} }{A_{2} }[/tex]

[tex]\frac{F_{1} }{0.0013}[/tex] = [tex]\frac{8.075}{0.00018}[/tex]

[tex]F_{1}[/tex] = [tex]\frac{0.0013 *8.075}{0.00018}[/tex]

    = 58.32

The minimum force that must be exerted on the piston is 58.32 N.

Answer:

5694000 min

Explanation:

Let's suppose the average American watches 4 hours of TV every day. First, we will calculate how many minutes they watch per day. We will use the conversion factor 1 h = 60 min.

(4 h/day) × (60 min/1 h) = 240 min/day

They watch 240 minutes of TV per day. Now, let's calculate how many minutes they watch per year. We will use the conversion factor 1 year = 365 day.

240 min/day × (365 day/year) = 87600 min/year

They watch 87600 min/year. Finally, let's calculate how many minutes they spend watching TV in 65 years.

87600 min/year × 65 year = 5694000 min

Answer:

Explanation:

The work done by an object can be found by using the formula

From the question

force = 500 N

distance = 4 m

We have

workdone = 500 × 4

We have the final answer as

Hope this helps you

Answer:

The acceleration of a small piece of ice is 10.40 m/s².

Explanation:

The electric force is given by:

[tex]F = Eq[/tex]

Where:    

E is the electric field = 1.07x10⁵ N/C

q is the charge = 1.05x10⁻¹¹ C          

The electric force is equal to Newton's second law:

[tex] Eq = ma [/tex]

Where:            

m is the mass = 1.08x10⁻⁴ g = 1.08x10⁻⁷ kg

a is the acceleration

Hence, the acceleration is:

[tex] a = \frac{Eq}{m} = \frac{1.07 \cdot 10^{5} N/C*1.05 \cdot 10^{-11} C}{1.08 \cdot 10^{-7} kg} = 10.40 m/s^{2} [/tex]

Therefore, the acceleration of a small piece of ice is 10.40 m/s².

I hope it helps you!                    

Answer:

a) The work done by gravity on the coin as it falls is 17.653 joules.

b) The kinetic energy of the coin at a speed of 60 meters per second is 10.8 joules.

c) The work lost due to air resistance is 6.853 joules.

d) The average force exerted on the coin due to air resistance as it fell is 0.023 newtons.

Explanation:

a) We must remind that situation with Earth-coin system must be represented by Principle of Energy Conservation and Work Energy Theorem. According to this latter, work done by gravity equals to the change in gravitational potential energy:

[tex]\Delta U_{g} = m\cdot g \cdot \Delta z[/tex] (Eq. 1)

Where:

[tex]\Delta U_{g}[/tex] - Change in gravitational potential energy, measured in joules.

[tex]m[/tex] - Mass, measured in kilograms.

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

[tex]\Delta z[/tex] - Height of the skyscraper, measured in meters.

If we know that [tex]m = 0.006\,kg[/tex], [tex]g = 9.807\,\frac{m}{s^{2}}[/tex] and [tex]\Delta z = 300\,m[/tex], the work done gravity on the coin is:

[tex]\Delta U_{g} = (0.006\,kg)\cdot \left(9.807\,\frac{m}{s^{2}} \right)\cdot (300\,m)[/tex]

[tex]\Delta U_{g} = 17.653\,J[/tex]

The work done by gravity on the coin as it falls is 17.653 joules.

b) By definition of translation kinetic energy, we get the following model:

[tex]K = \frac{1}{2}\cdot m\cdot v^{2}[/tex]

Where:

[tex]K[/tex] - Kinetic energy of the coin right before hitting the street, measured in joules.

[tex]v[/tex] - Speed of the coin, measured in meters per second.

If we get that [tex]m = 0.006\,kg[/tex] and [tex]v = 60\,\frac{m}{s}[/tex], the kinetic energy at this speed is:

[tex]K = \frac{1}{2}\cdot (0.006\,kg)\cdot \left(60\,\frac{m}{s} \right)^{2}[/tex]

[tex]K = 10.8\,J[/tex]

The kinetic energy of the coin at a speed of 60 meters per second is 10.8 joules.

c) The work lost due to air resistance is obtained derived from Principle of Energy Conservation and Work-Energy Theorem:

[tex]W_{lost} = \Delta U_{g}-K[/tex] (Eq. 2)

Where [tex]W_{lost}[/tex] is the work lost due to air resistance, measured in joules.

If we know that [tex]\Delta U_{g} = 17.653\,J[/tex] and [tex]K = 10.8\,J[/tex], the work lost due to air resistance is:

[tex]W_{lost} = 17.653\,J-10.8\,J[/tex]

[tex]W_{lost} = 6.853\,J[/tex]

The work lost due to air resistance is 6.853 joules.

d) The average force exerted on the coin due to air resistance can be determined by applying definition of work, as air resistance force was antiparallel to the displacement of the coin. That is:

[tex]W_{lost} = F\cdot \Delta z[/tex]

[tex]F = \frac{W_{lost}}{\Delta z}[/tex] (Eq. 3)

Where [tex]F[/tex] is the average force exerted on the coin due to air resistance, measured in newtons.

If we know that [tex]W_{lost} = 6.853\,J[/tex] and [tex]\Delta z = 300\,m[/tex], then the average force exerted on the coin is:

[tex]F = \frac{6.853\,J}{300\,m}[/tex]

[tex]F = 0.023\,N[/tex]

The average force exerted on the coin due to air resistance as it fell is 0.023 newtons.

Answer:

leather

Explanation:

plz mark as brainliest......hope it helps

Answer:

a. leather

Explanation:

Hello friend!!!!

a. leather is the correct option because jute, wool and cotton are all natural fibres whereas leather is a synthetic fibre.

Hope this helps

plz mark as brainliest!!!!!!

Answer:

a- More heat is required for the constant-pressure process than for the constant-volume

Explanation:

we have to solve using the thermodynamic first law. this is the heat applied to the system

dQ = dU + dW

definition of terms:

dU = change in internal energy

dW = work done

we have it that

change in internal energy dU is directly proportional to work done dW

but when we are in constant volume process, work done of the gas is zero

therefore

dQ of constant pressure is > than that of constant volume

so constant pressure process requires more heat

The process that requires more heat is the constant-pressure process than the constant-volume process.

According to the first law of thermodynamics, the heat that's applied to the system will be the addition of the change in internal energy and the work done.

In a constant-volume process, the work done on the gas is equal to zero. More heat will be required for the constant-pressure process than for the constant-volume process.

Also, it should be noted that the change in the thermal energy of the gas will be the same for the constant-pressure process and the constant-volume process.

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Answer:

In the absence of thrust, the lunar lander moves downward toward the surface of the moon. At this point, the only force acting on the lunar lander is gravity, which is directed toward the center of the moon. Because the net force is in the downward direction, the lunar lander moves downward.

Explanation: plato

Answer: In the absence of thrust, the lunar lander moves downward toward the surface of the moon. At this point, the only force acting on the lunar lander is gravity, which is directed toward the center of the moon. Because the net force is in the downward direction, the lunar lander moves downward.

Explanation: edmentum sample answer

Answer:

The correct answer is A. A government that wants to increase its GDP would most likely increase the money supply to make it easier to borrow money.

Explanation:

If the government wanted to increase its GDP, the most appropriate way to do so would be to increase the money supply both through issuance and through a reduction in bank reserve requirements, thereby increasing the circulating money in the hands of society.

This, in turn, would make citizens reinvest that money, increasing economic production and, therefore, the national GDP.

Answer: A. Increase the money supply to make it easier to borrow money

Explanation: I just took the test on Ap ex

Taking into account the definition of wavelength, frecuency and propagation speed, the frequency is 5 Hz.

Wavelength (λ) is the distance between two consecutive points that are in the same state of vibration (the state of vibration is called phase). It is expressed in units of length (m).

Frequency (f) is the number of waves per unit of time and is normally expressed in Hertz (Hz) which is the number of waves per second.

The velocity of propagation is the speed with which the wave propagates in the medium. Relate the wavelength (λ) and the frequency (f) inversely proportional using the following equation:

v = f * λ

In this case, you know:

Replacing in the previous expression:

50 m/s= f× 10 cm

Solving;

f= 50 m/s÷ 10 cm

f= 5 Hz

Finally, the frequency is 5 Hz.

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The answer is A I Hope this answer helps you (i got the question right)

Answer:

A. As speed increases, kinetic energy increases exponentially.

Explanation:

The amount of kinetic energy an object has depends on the speed. Kinetic energy is also known as "motion energy." This being said, if speed is increasing, decreasing, or staying constant, the kinetic energy of the object will too.

Answer:

This answer was wrong

Explanation:

I took the test and I missed this question.  So it is not answer B: pass a literacy test.  

It will need an A. pass a vision and hearing test

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Answer:

Maybe.

Explanation:

Answer:

What do you mean ma´am/sir?

Explanation:

Answer: a tendency to do nothing or to remain unchanged.

Explanation:

For example, if you roll a ball, it will continue rolling unless friction or something else stops it by force.

Answer:

the property of matter by which it retains its state of rest or its velocity along a straight line so long as it is not acted upon by an external force. an analogous property of a force: electric inertia.

or a tendency to do nothing or to remain unchanged.

Answer:

A) v3 = -[6.29 × 10^(6)]j^ - [7.06 × 10^(6)]i^

B) K_total = 373.08 × 10^(-15) J

Explanation:

We are given;

Mass of unstable atomic nucleus; M = 1.83 × 10^(-26) kg

Mass of first particle; m1 = 5.03 × 10^(-27) kg

Speed of first particle in y-direction; v1 = (6 × 10^(6) m/s) j^

Mass of second particle; m2 = 8.47 × 10^(-27) kg

Speed of second particle in x - direction; v2 = (4 × 10^(6) m/s) i^

Now, we don't have the mass of the third particle but since we are told the unstable atomic nucleus disintegrates into 3 particles, thus;

M = m1 + m2 + m3

1.83 × 10^(-26) = (5.03 × 10^(-27)) + (8.47 × 10^(-27)) + m3

m3 = (1.83 × 10^(-26)) - (13.5 × 10^(-27))

m3 = 4.8 × 10^(-27) kg

A) Applying law of conservation of momentum, we have;

MV = (m1 × v1) + (m2 × v2) + (m3 × v3)

Now, the unstable atomic nucleus was at rest before disintegration, thus V = 0 m/s.

Thus, we now have;

0 = (m1 × v1) + (m2 × v2) + (m3 × v3)

We want to find the velocity of the third particle v3. Let's make it the subject of the formula;

v3 = [(m1 × v1) + (m2 × v2)]/(-m3)

Plugging in the relevant values, we have;

v3 = [(5.03 × 10^(-27) × 6 × 10^(6))j^ + (8.47 × 10^(-27) × 4 × 10^(6))i^]/(-4.8 × 10^(-27))

v3 = [(30.18 × 10^(-21))j^ + (33.88 × 10^(-21))i^]/(-4.8 × 10^(-27))

v3 = -[6.29 × 10^(6)]j^ - [7.06 × 10^(6)]i^

B) Formula for kinetic energy is;

K = ½mv²

Now,total kinetic energy is;

K_total = K1 + K2 + K3

K1 = ½ × 5.03 × 10^(-27) × (6 × 10^(6))²

K1 = 90.54 × 10^(-15) J

K2 = ½ × 8.47 × 10^(-27) × (4 × 10^(6))²

K2 = 67.76 × 10^(-15)

To find K3, let's first find the magnitude of v3 because it's still in vector form.

Thus;

v3 = √[(-6.29 × 10^(6))² + (-7.06 × 10^(6))²]

v3 = 9.46 × 10^(6) m/s

K3 = ½ × 4.8 × 10^(-27) × (9.46 × 10^(6))²

K3 = 214.78 × 10^(-15) J

K_total = (90.54 × 10^(-15)) + (67.76 × 10^(-15)) + (214.78 × 10^(-15))

K_total = 373.08 × 10^(-15) J

Answer:

Explanation:

Electrons are allowed "in between" quantized energy levels, and, thus, only specific lines are observed. FALSE. The specific lines are obseved because of the energy level transition of an electron in an specific level to another level of energy.

The energies of atoms are not quantized. FALSE. The energies of the atoms are in specific levels.

When an electron moves from one energy level to another during absorption, a specific wavelength of light (with specific energy) is emitted. FALSE. During absorption, a specific wavelength of light is absorbed, not emmited.

Electrons are not allowed "in between" quantized energy levels, and, thus, only specific lines are observed. TRUE. Again, you can observe just the transition due the change of energy of an electron in the quantized energy level

When an electron moves from one energy level to another during emission, a specific wavelength of light (with specific energy) is emitted. TRUE. The electron decreases its energy releasing a specific wavelength of light.

The energies of atoms are quantized. TRUE. In fact, the energy of all subatomic, atomic, and molecular particles is quantized.

The reason why atoms emit only specific wavelengths is because the energy levels in atoms are quantized.

Max Plank introduced the idea of quantization of energy in the early 1900s. He introduced the idea that energy can only take on certain specific values. This idea was later extended to atoms by Neils Bohr.

The following statements explain why atoms only emit certain wavelengths of light when they are excited;

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Answer:

Yes

Explanation:

The variables change in and experiment.

Answer:

If you are carefully enough to control everything, then everything that could change the result of your experiment won't happen.

Explanation:

Complete Question

The compete question is shown on the first uploaded question

Answer:

The speed is  [tex]  v  =  350 \  m/s [/tex]  

Explanation:

From the question we are told that

   The  distance of separation is  d =  4.00 m  

  The distance of the listener to the center between the speakers is  I =  5.00 m

  The change in the distance of the speaker is by [tex]k  =  60 cm  =  0.6 \  m[/tex]

    The frequency of both speakers is [tex]f =  700 \  Hz[/tex]

Generally the distance of the listener to the first speaker is mathematically represented as

       [tex]L_1  =  \sqrt{l^2 + [\frac{d}{2} ]^2}[/tex]

       [tex]L_1  =  \sqrt{5^2 + [\frac{4}{2} ]^2}[/tex]

        [tex]L_1  =   5.39 \  m [/tex]

Generally the distance of the listener to second speaker at its new position is  

          [tex]L_2  =  \sqrt{l^2 + [\frac{d}{2} ]^2 + k}[/tex]

       [tex]L_2  =  \sqrt{5^2 + [\frac{4}{2} ]^2 + 0.6}[/tex]

        [tex]L_2  =   5.64  \  m [/tex]  

Generally the path difference between the speakers is mathematically represented as

        [tex]pD  = L_2 - L_1  =  \frac{n  *  \lambda}{2}[/tex]

Here [tex]\lambda[/tex] is the wavelength which is mathematically represented as

         [tex]\lambda =  \frac{v}{f}[/tex]

=>    [tex] L_2 - L_1  =  \frac{n  *  \frac{v}{f}}{2}[/tex]

=>    [tex] L_2 - L_1  =  \frac{n  *  v}{2f}[/tex]  

=>    [tex] L_2 - L_1  =  \frac{n  *  v}{2f}[/tex]  

Here n is the order of the maxima with  value of  n =  1  this because we are considering two adjacent waves

=>    [tex]  5.64 - 5.39   =  \frac{1  *  v}{2*700}[/tex]      

=>    [tex]  v  =  350 \  m/s [/tex]  

The speed of sound in air is 350 m/s

Since the distance between both speakers is 4 m, and the listener is standing 5 m away from halfway between them, the distance L from each loudspeaker to the listener, since the arrangement forms a right-angled triangle, using Pythagoras' theorem,

L = √[(5 m)² + (4/2 m)²]

= √[25 m² + (2 m)²]

= √[25 m² + 4 m²]

= √29 m² = 5.39 m.

Now, when one speaker is moved 60 cm = 0.6 m away from its original position, its distance from the listener is now

L' = √[(5 m)² + (4/2 + 0.6 m)²]

= √[25 m² + (2 m + 0.6 m)²]

= √[25 m² + (2.6 m)²]

= √[25 m² + 6.76 m²]

= √31.76 m²

= 5.64 m.

Now, the path difference when we first have destructive interference is

ΔL = L' - L

= 5.64 - 5.39

= 0.25

Since we have destructive interference for the first time when the speaker is moved, the path difference, ΔL = (n + 1/2)λ where λ = wavelength = v/f where v = speed of sound in air and f = frequency = 700 Hz.

Now, since we have destructive interference for the first time, n = 0.

So,  ΔL = (n + 1/2)λ

ΔL = (0 + 1/2)v/f

ΔL = v/2f

Making v subject of the formula, we have

v = 2fΔL

Substituting the values of the variables into the equation, we have

v = 2fΔL

v = 2 × 700 Hz × 0.25 m

v = 350 m/s

So, the speed of sound in air is 350 m/s

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Complete Question

The complete question is shown on the first uploaded image

Answer:

The expression for the velocity of the sixth ball is

 [tex]v_2 = \frac{u_1 sin\theta }{sin \phi cos\theta + cos \phi sin\theta}[/tex]

Explanation:

From the question we are told that

     The mass of the 8 ball is  [tex]m_1 =  0.5 \  kg[/tex]

      The initial velocity of the 8 ball is  [tex]u_1  =  3.7 \  m/s[/tex]

      The initial velocity of the 6 ball is  [tex]u_2  =  0  \  m/s[/tex]

         The mass of the 6 ball is  [tex]m_2 =  0.5 \  kg[/tex]

Generally from the law of momentum conservation is  

     [tex]m_1 *u_1 + m_2 * u_2 = m_1 * v_1 +m_2 *v_2[/tex]

Now along the y  axis

      [tex]u_1 =u_y_1 =  0 \  m/ s[/tex]

      [tex]u_2 =u_y_2=  0 \  m/ s[/tex]

      [tex]v_1 =v_y_1=  v_1 sin \theta  \  m/ s[/tex]

      [tex]v_2 =v_y_2=  v_2 sin \phi  \  m/ s[/tex]

So

  [tex]m_1 *0 + m_2 * 0 = m_1 * (v_1 sin \theta) +m_2 *(v_2 sin \phi )[/tex]

=>  [tex]v_1 = \frac{v_2 sin \phi }{ sin \theta}[/tex]

Now along the x  axis

      [tex]u_1 =u_x_1 =  u_1 \  m/ s[/tex]

       [tex]u_2 =u_2_2=   0 \  m/ s[/tex]

        [tex]v_1 =v_x_1=  v_1 cos \theta  \  m/ s[/tex]

        [tex]v_2 =v_x_2=  v_2 cos \phi  \  m/ s[/tex]

So

        [tex]m_1 *u_1 + m_2 * 0 = m_1 *(v_1 cos \theta) +m_2 *(v_2 cos \phi)[/tex]

=>[tex]m_1 *u_1  = m_1 *(v_1 cos \theta) +m_2 *(v_2 cos \phi)[/tex]    

substituting for [tex]v_1[/tex] in the above equation

=>[tex]m_1 *u_1  = m_1 *([ \frac{v_2 sin \phi }{ sin \theta}] cos \theta) +m_2 *(v_2 cos \phi)[/tex]      

=>[tex]m_1 *u_1  = m_1 *([ \frac{v_2 sin \phi }{ sin \theta}] cos \theta) +m_2 *(v_2 cos \phi)[/tex]

 given that  [tex]m_1 = m_2 = m[/tex]

=>[tex]m *u_1  = m *([ \frac{v_2 sin \phi }{ sin \theta}] cos \theta) +m *(v_2 cos \phi)[/tex]

=>[tex]m *u_1  = m [([ \frac{v_2 sin \phi }{ sin \theta}] cos \theta) + (v_2 cos \phi)][/tex]

=>[tex]u_1  = ([ \frac{v_2 sin \phi }{ sin \theta}] cos \theta) + (v_2 cos \phi)[/tex]

=>[tex]u_1  = v_2 sin\phi cot \theta + v_2 cos\phi [/tex]

[tex]v_2 = \frac{u_1  }{sin\phi cot\theta + cos\phi }[/tex]

converting [tex]cot \phi[/tex] back  to  [tex]\frac{cos \theta}{sin\theta }[/tex]

So

    [tex]v_2 = \frac{u_1  }{sin\phi [\frac{cos \theta}{sin\theta }] + cos\phi }[/tex]

multiply through by  [tex]\frac{sin \theta}{sin \theta }[/tex]

   [tex] \frac{sin \theta}{sin \theta } *v_2 = \frac{sin \theta}{sin \theta } * \frac{u_1  }{sin\phi [\frac{cos \theta}{sin\theta }] + cos\phi }[/tex]

=>  [tex]v_2 = \frac{u_1 sin\theta }{sin \phi cos\theta + cos \phi sin\theta}[/tex]