A 2 kg melon is balanced on your bald uncle’s head. His son, Throckmorton, shoots a 50 g (0.05kg) arrow at it with a speed of 30 m/s. The arrow passes through the melon and emerges with a speed of 18 m/s. Find the speed of the melon as it flies off the man’s head.

The speed of the melon as it flies off the man’s head is 0.3 m/s.

Explanation:

Given;

mass of the melon, m₁ = 2 kg

initial speed of the melon, u₁ = 0

mass of arrow, m₂ = 0.05 kg

initial speed of the arrow, u₂ = 30 m/s

final speed of the arrow, v₂ = 18 m/s

let v₁ be the final speed of the melon as it flies off the man's head.

Apply the principle of conservation of linear momentum;

m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂

2(0) + 0.05 x 30 = 2v₁  + 0.05 x 18

1.5 = 2v₁ + 0.9

2v₁ = 1.5 - 0.9

2v₁ = 0.6

v₁ = 0.6 / 2

v₁ = 0.3 m/s

Therefore, the speed of the melon as it flies off the man’s head is 0.3 m/s.