Question

A 6.5×10−2 kg arrow hits the target at 25 m/s and penetrates 3.8 cm before stopping.
A) What average force did the target exert on the arrow? B)What average force did the arrow exert on the target? C)An identical arrow strikes the target at 65m/s . If the target exerts the same average force as before, what's the penetration depth?

Answer 1

funny how I keep seeing the same problems, I just solved this for someone else

for some reason this kinematic equation gets no love\[v_f^2=v_i^2+2ad\]in this case the final velocity is zero, and acceleration is in the opposite direction as velocity, so this becomes\[0=v_i^2-2ad\]since two of the variables are given in the problem you can find acceleration from this equation. once you know the acceleration you can find the force with\[F=ma\]for the next part use the same equations, but work it backwards:
calculate the new acceleration from F=ma then use the kinematic above to find the distance d