Question

An astronaut with a mass of 90 kg (including spacesuit and equipment) is drifting away from his spaceship at a speed of 0.20 m/s with respect to the spaceship. The astronaut is equipped only with a 0.50-kg wrench to help him get back to the ship.

A). With what speed must he throw the wrench for his body to acquire a speed of 0.10 m/s?
B). In what direction relative to the spaceship must he throw the wrench? Towards the spaceship or away from the spaceship.

Answer 1

Part A:

`v_w=53.9\ m/s`

Part B:

Wrench is thrown away from the spaceship

Explanation:

This the problem related to conservation of momentum.

According to the conservation of momentum:

Initial Momentum=Final Momentum

`m_av_a=m_wv_w+(m_a-m_v)v`

where:

`m_a` is the mass of astronaut

`m_w` is the mass of wrench

`m_a-m_w` is the mass when wrench is thrown

`v_a` is the speed of astronaut

`v_w` is the speed of wrench

v is the speed acquired

Part A:

(+ve sign for away from ship),( -ve sign for towards ship)

v= -0.10 m/s

`90*0.2=0.5*v_w+(90-0.5)(-0.1)\\v_w=53.9\ m/s`

Part B:

Since velocity is +ve as calculated above and according to conditions:

• +ve sign for away from ship

• -ve sign for towards ship

Wrench is thrown away from the spaceship