Question

William Tell shoots an apple from his son's head. The speed of the 142-g arrow just before it strikes the apple is 23.9 m/s, and at the time of impact it is traveling horizontally. If the arrow sticks in the apple and the arrow/apple combination strikes the ground 8.00 m behind the son's feet, how massive was the apple? Assume the son is 1.85 m tall.

Answer 1

Momentum is conserved. Let’s determine the initial momentum.
M = 0.142* 23.9 = 3.3938 Kg m/s

As the apple falls 1.85 meters, it moves a horizontal distance of 8 meters. To determine the horizontal velocity of the apple and arrow, we need to determine the time it is falling. Use the following equation.

d = vi * t + ½ * a * t^2, vi = 0, a = 9.8
1.85 = ½ * 9.8 * t^2
t = √(1.85/4.9)

v = 8 ÷ √(1.85/4.9) = 13.02 m/s
Final momentum = m * 8 ÷ √(1.85/4.9)
m * 8 ÷ √(1.85/4.9) = 3.3938
m = 0.261 Kg

This is mass of the apple and the arrow.
Apple = [3.3938 * √(1.85/4.9) ÷ 8] – 0.142
This is approximately 0.118 Kg