Answer to Question #228209 in Physics for Ekott jnr

Question

A 70kg astronaut is floating free in space several metres from her aircraft. She is holding a 1.6kg wrench which she can hurl with a speed of 22m/s.
1) in which direction should she hurl the wrench so she can move towards the spacecraft
2) what would be her speed towards the spacecraft?

Answer 1

Given:

$M=70\:{\rm kg},\quad m=1.6\:{\rm kg},\quad u=22\:\rm m/s$

1) in the opposite direction to the spacecraft.

2) the law of conservation of momentum gives

$$0=Mv-mu\\ v=\frac{m}{M}u=\frac{1.6}{70}*22=0.5\:\rm m/s$$