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Enharmonics

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Hey all, first time poster here. I'm pretty confused about how exactly to use conservation of momentum and kinetic energy to work collision problems, specifically perfectly inelastic collisions (you could probably tell it was that kind, since K is conserved).

I'm actually stuck on two different questions, which is why I decided to post and see if someone here could maybe steer me in the right direction as to how to work these.

A billiard ball traveling at 3.00 m/s collides perfectly elastically with an identical billiard ball initially at rest on the level table. The initially moving billiard ball deflects 30.0° from its original direction. What is the speed of the initially stationary billiard ball after the collision?

So I've got

##V_{1,i} = 3.00 \frac{m}{s} , V_{2,i} = 0 , m_1 = m_2 = m##

##P_i = P_f , K_i = K_f##

Because the initially moving billiard ball deflects 30.0°, I set up my conservation of momentum equation with an X and Y-component, so that

## P_x: m(3.00 \frac{m}{s}) + 0 = mV_{1,f}cos(30.0°) + mV_{2,f,x}##

and

## P_y: 0 = V_{1,f}sin(30.0°) - V_{2,f,y} ##

Of course, the m's in ##P_x## can cancel, since ##m_1 = m_2##. I don't know either the first or second ball's final velocities or even the direction angle at which the second ball ##m_2## moves after the collision. In the diagram I've drawn on my paper I just have the first ball moving along the x-axis and deflecting "upward" at an angle of 30.0°, with the second ball deflecting "downward" at some angle ##\theta##.

I tried using conservation of kinetic energy, but that just leaves me with

##\frac{1}{2}(3.00 \frac{m}{s})^2 + 0 = \frac{1}{2}V_{1,f} + \frac{1}{2}V_{2,f}##

which I can't solve for the target variable V_{2,f} because I only have V_{1,f} in terms of its components. I don't know what to do at this point.

I'm actually stuck on two different questions, which is why I decided to post and see if someone here could maybe steer me in the right direction as to how to work these.

1. Homework Statement

1. Homework Statement

A billiard ball traveling at 3.00 m/s collides perfectly elastically with an identical billiard ball initially at rest on the level table. The initially moving billiard ball deflects 30.0° from its original direction. What is the speed of the initially stationary billiard ball after the collision?

So I've got

##V_{1,i} = 3.00 \frac{m}{s} , V_{2,i} = 0 , m_1 = m_2 = m##

## Homework Equations

##P_i = P_f , K_i = K_f##

## The Attempt at a Solution

Because the initially moving billiard ball deflects 30.0°, I set up my conservation of momentum equation with an X and Y-component, so that

## P_x: m(3.00 \frac{m}{s}) + 0 = mV_{1,f}cos(30.0°) + mV_{2,f,x}##

and

## P_y: 0 = V_{1,f}sin(30.0°) - V_{2,f,y} ##

Of course, the m's in ##P_x## can cancel, since ##m_1 = m_2##. I don't know either the first or second ball's final velocities or even the direction angle at which the second ball ##m_2## moves after the collision. In the diagram I've drawn on my paper I just have the first ball moving along the x-axis and deflecting "upward" at an angle of 30.0°, with the second ball deflecting "downward" at some angle ##\theta##.

I tried using conservation of kinetic energy, but that just leaves me with

##\frac{1}{2}(3.00 \frac{m}{s})^2 + 0 = \frac{1}{2}V_{1,f} + \frac{1}{2}V_{2,f}##

which I can't solve for the target variable V_{2,f} because I only have V_{1,f} in terms of its components. I don't know what to do at this point.

__[Mentor note: Second problem removed. Member asked to start a new thread for the second problem]__
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