An archer shoots an arrow toward a 300 g target that is sliding in her direction

Question

An archer shoots an arrow toward a 300 g target that is sliding in her direction at a speed of 2.10 m/s on a smooth, slippery surface. The 22.5 g arrow is shot with a speed of 35.5 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? ____________ m/s An archer shoots an arrow toward a 300 g target that is sliding in her direction at a speed of 2.10 m/s on a smooth, slippery surface. The 22.5 g arrow is shot with a speed of 35.5 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? ____________ m/s

Explanation / Answer

starting momentum:

(22.5 g)(35.5 m/s) = 798.75 g m/s        for the arrow

(300 g)(-2.10 m/s) = -630 g m/s        for the target

Total starting momentum: 168.75 g m/s

We know momentum is conserved, and the ending momentum for the target is 0, since it stops. So the ending momentum for the arrow has to be 168.75 g m/s. So its speed is:

(168.75 g m/s)/(22.5 g) = 7.5 m/s

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