The target loses momentum in the opposite direction to the arrow's motion, by an amount 300 g*2.35 m/s = 705 g m/s.
The arrow loses momentum equal to that, in the direction of its motion. Divide 705 g m/s by 22.5 g to get the decrease in the arrow's velocity. Then subtract that from the inital velocity.
Or just solve this equation:
Arrow mass*Initial arrow speed
-Target mass * Initial target speed = Arrow mass*Final arrow speed
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?
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