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
