Push away problem

Question

An 80 kg astronaut floating in space is 30 m away from his spaceship. He wants to return to his spaceship in 10 s. With how much speed must he throw his 2 kg space hammer, directly away from the spaceship to accomplish the task?

Answer 1

Use Conservation of Momentum and write that 80Vastronaut inital +2Vhammer initial = 80Vastronaut final -2Vhammer final =0 since initial velocities =0 (assign the + direction to be toward the spacecraft). Additionally the Astronaut wants to move 30 meters in 10 seconds after throwing the hammer so Vastronaut final = 30/10=3 m/s. Solve the momentum equation using Vastronaut final =3 m/s finding that Vhammer final = 120 m/s.