A 30.0 g arrow is shot by William Tell though an 8.00 cm thinck apple sitting on top of his son's head. If the arrow enters the apple at 30.0 m/s and emerges at 25.0 m/s in the same direction, with what force has the apple resisted the arrow?

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The resisting force of the apple, causes an impulse into the arrow. The change of momentum of the arrow is then equal to the impulse.

dp = F dt

F = dp/dt

The change of momentum is just

dp = mv2 - mv1 = m (v2 - v1).

The amount of time,

dt = dist / v_ave

dt = dist / ((v1 + v2) / 2)

Therefore,

F = m (v2 - v1) / dist * (v1 + v2) / 2

F = 1/2 * m (v2^2 - v1^2) / dist

F = 1/2 * 30e-3 * (30^2 - 25^2) / 8e-3

F = 515.625 N