Question

An unfortunate astronaut finds himself stranded in space 15.0 meters away from his spacecraft, completely motionless with respect to the spacecraft. Since he cannot walk or swim in space, he recalls some basic physics and decides to take a 0.500 kg tool from his belt and launch it away from the craft, expecting his recoil will move him toward the spacecraft. If the astronaut's mass is 120 kg and he can throw the tool at a speed of 30.0 m/s, how long will it take him to reach the spacecraft? Start by using the law of Conservation of Linear Momentum.

Answer 1

Mass of the astronaut, M = 120 kg

Mass of the tool, m = 0.50 kg

Velocity of the tool, v = 30.0 m/s

Velocity of the atronaut, V = ?

Initially the astronaut is standstill.

So, initial momentum, Pi = 0

Final momentum, Pf = m*v + M*V

From conservation of momentum -

Pi = Pf

=> 0 = m*v + M*V

=> 0 = 0.500*30.0 + 120*V

=> V = -(0.500*30.0) / 120 = -0.125 m/s

This is the recoil velocity of the astronaut.

Distance between the astronaut and the spacecraft = d = 15.0 m

Hence, time taken by the astronaut to reach the spacecraft, t = d/V = 15.0 / 0.125 = 120 s (Answer)