Question

A man of mass 80kg stands next to a stationary ball of mass 4kg on a frictionless surface. He kicks the ball forward along the surface with a speed 15m/s. Calculate the man’s recoil speed

Answer 1

Momentum is conserved.

p = m₁v₁ + m₂v₂ = constant

Momentum before the collision(kick):

p = 80 * 0 + 4 * 0 = 0

Momentum after the collision:
p = 80 * v₁ + 4 * 15 = 0

Solve for v₁.

Answer 2

The recoil speed of the man is 0.75 m/s

Recoil speed: This is the speed of the man after impact with the ball.

Using,

Newton's third law of motion: To every action, there is an equal and opposite reaction.

From the question,

The momentum of the man = momentum of the ball

MV = mv............... Equation 1

Where M = mass of the man, V = recoil speed of the man, m = mass of the ball, v = final speed of the ball after impact.

Therefore,

V = mv/M ............. Equation 2

Given: M = 80 kg, m = 4 kg, v = 15 m/s

Substitute these values into equation 2

V = (4×15)/80

V = 60/80

V = 0.75 m/s

Hence, the man's recoil speed is 0.75 m/s.

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