identify mass, velocity, and unknown

Question

The mass of ball A is 10 kilograms and the mass of ball B is 5 kilograms. If
the initial velocity is set to 3 meters per second for each ball, what is the
final velocity of ball B if the final velocity of ball A is 2 meters per second?
Use the elastic collision equation to find the final velocity of ball B. Assume
ball A initially moves from right to left and ball B moves in the opposite
direction. Identify each mass, velocity, and unknown. Show your work,
including units, and indicate the direction of ball B in your answer.

Answer 1

Since no angles are given we will assume this is a 1 dimensional problem.

An elastic collision conserves both momentum and kinetic energy.

So 2 equations can be written equating "Before" and "After" for p and KE

Intuitively, ball A, being heavier than ball B, will continue in its direction

and not bounce back, so its velocity will be positive 

10(3) - 5(3) = 10(2) + 5(vf)

vf = - 1 m/s

If the problem had not given ball A final velocity, then

the 2nd equation for KE would be needed.