# Billiard ball collision with change in direction

1. Nov 7, 2008

### mariac

1. The problem statement, all variables and given/known data

A billiard ball with mass 0.210 kg has a speed of 5.2 m/s and collides completely inelastically with another ball of the same size and mass.

A. Find the final speed of the two balls.
The answer I got was 2.6 m/s. The next part is trickier.

B. Another billiard ball traveling at 6.25 m/s collides with a second stationary ball of equal size and shape causing the second ball to move at an angle of 25 degrees with respect to the horizontal at a speed of 3.0 m/s.

What impulse (magnitude and direction) did the each ball receive? What is the final velocity (magnitude and direction ) of the first ball?

2. Relevant equations

3. The attempt at a solution

Conceptually, I don't understand why the second ball would move at an angle. Would that mean that the first ball hits the second ball off-center? I know that the total momentum must remain the same, and p=6.25m/s x 0.210kg = 1.31kg m/s. Would this be the magnitude of the impulse received by the second ball? Or would the impulse be only half of this since the first ball receives an equal impulse? If the first ball hit the second slightly off center, this would change the direction of the impulse. I presume the first ball would turn 25 degrees below horizontal after the collision. Would the first ball proceed at a velocity of 3.25 m/s, or would the change in direction somehow affect the velocity?
I'm really confused. Can you help?
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Nov 7, 2008

### krausr79

I don't have much experience w/ impulse, but your guesses seem correct. It would be an off-center hit to cause this. To find out the direction/magnitude of the first ball, break it into x-y components. In both an x and y sense seperately, Start momenta added together should equal final momenta added together. You can find out the starting momenta of both balls, and the final momentum of the second ball; which will allow you to solve for the final momentum of the second ball. Done in x and y you will have components, then you can switch it back to polar (direction, magnitude).