Question

An archer shoots an arrow toward a 300 g target that is sliding in her direction at a speed of 2.35 m/s on a smooth, slippery surface. The 22.5 g arrow is shot with a speed of 41.0 m/s and passes through the target, which is stopped by the impact. What is the speed of the arrow after passing through the target?

Answer 1

the change of momentum of the arrow will be the same as the change of momentum of the target
initial target momentum = 0.300 * 2.35 = .705 kg m/s
final target momentum = 0
so the arrow momentum will be reduced by .705 kg m/s
final arrow momentum = .0225*41 - .705
= .2175 kg m/s
final arrow speed = .2175/.0225 = 9.67 m/s