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.

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wagonbelleville wagonbelleville · Answer 1 · 2019-12-12T09:50:09+01:00

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

[tex]h = u t + \dfrac{1}{2}gt^2[/tex]

[tex]h = \dfrac{1}{2}gt^2[/tex]

[tex]t = \sqrt{\dfrac{2h}{g}}[/tex]

[tex]t = \sqrt{\dfrac{2\times 1.85}{9.8}}[/tex]

t = 0.614 s

[tex]speed = \dfrac{distance}{time}[/tex]

[tex]s = \dfrac{9.30}{0.614}[/tex]

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