Question

Ask Your Teacher William Tell shoots an apple from his son's head. The speed of the 120-g arrow just before it strikes the apple is 29.7 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 9.30 m behind the son's feet, how massive was the apple? Assume the son is 1.85 m tall.

Answer 1

Answer:

 M = 0.115 kg

Explanation:

given,

mass of arrow = 120 g = 0.12 Kg

speed of arrow before it strike apple = 29.7 m/s

distance traveled by the arrow stick combination = 9.30 m

height of the son = 1.85 m

weight of the apple = ?

now,

time of flight of arrow and apple combination

using equation of motion

$h = u t + \dfrac{1}{2}gt^2$

$h = \dfrac{1}{2}gt^2$

$t = \sqrt{\dfrac{2h}{g}}$

$t = \sqrt{\dfrac{2\times 1.85}{9.8}}$

t = 0.614 s

$speed = \dfrac{distance}{time}$

$s = \dfrac{9.30}{0.614}$

    s = 15.15 m/s

using conservation of momentum

 m v = (M+ m) s

 0.12 x 29.7 = (M+ 0.12) x 15.15

 M+ 0.12 = 0.235

 M = 0.115 kg

mass of apple is equal to 0.115 Kg