Physics Question with Collisions?

Question

A softball of mass 0.220 kg that is moving with a speed of 8.5 m/s (in the positive direction) collides head-on and elastically with another ball initially at rest. Afterward the incoming softball bounces backward with a speed of 3.7 m/s.

(a) Calculate the velocity of the target ball after the collision.
(b) Calculate the mass of the target ball.

Answer 1

Linear momentum is conserved.

The initial momentum is

(.220 kg)(8.5 m/s) + 0

The final momentum is

(.220 kg)(-3.7 m/s) + mv

where m and v are the mass and velocity of the second ball.
The equation to solve is then

(.220)(8.5) = (.220)(-3.7) + mv

You can solve this for the product mv, but can't get m or v individually unless the collision is PERFECTLY elastic. If that's the case, kinetic energy is also conserved:

Initial kinetic energy = final kinetic energy

1/2 (.220) (8.5 ^ 2) = 1/2 (.220) (3.7 ^ 2) + 1/2 m v ^ 2

Now you have two equations and two unknowns and can solve for both m and v. But again, this is only correct if the collision is perfectly elastic.