Which way will target move after collision?

Question

A bullet with a mass of 500 g is traveling at 250m/s to the right. It hits a stationary target head on. The targets mass is 25.0 kg and it rests on a smooth surface. The bullet bounces backwards (to the left) off the target at 100m/s

A) which way must the move after the collision. right, left stationary, or unable to tell from data given.

b) determine the recoil speed of the target after the collision.

Answer 1

Pi = .5*250 = 125 kg∙m/s

A)  The target will move to the right

B)  Vt = (125 + 50)/25 = 7 m/s

Answer 2

I am assuming that the bullet's bounce is measured relative to the earth and not to the recoiling target.

We can use conservation of momentum to solve the problem.  Before collision, the entire momentum resides in the (very large) 500 g bullet, which is moving only a little less than the speed of sound (very fast for such a large bullet).  The bullet's momentum is 0.500 kg * 250 m/s or 125 kg∙m/s to the right.  Just after the collision, the system's momentum is still 125 kg∙m/s, but the bullet's momentum is now 0.500 kg * -100 m/s, or -50 kg∙m/s.  The remaining 175 kg∙m/s momentum must therefore be in the target.  At a mass of 25.0 kg, it must be moving to the right at 175 kg∙m/s / 25.0 kg, or 7.00 m/s.