Question

An astronaut whose mass is ma= 100kg is initially at rest. His colleague throws him a wrench of mass mw= 5kg at a velocity Vw= 5m/s. What is the velocity (magnitude and direction) of the astronaut after he catches the wrench?

Answer 1

The total momentum of the astronaut holding the wrench is the same as the sum of the momenta of the astronaut initially and the wrench moving toward him.  That is, total linear momentum is always conserved.  So initially:

$p_{a}=m_{a}v_{a}=100kg \times 0 \frac{m}{s}=0 \\ p_{w}=m_{w}v_{w}=5kg \times 5 \frac{m}{s}=25\frac{kgm}{s}$

This will be the momentum of the astronaut holding the wrench afterward:

$p_{a+w}=m_{a+w}v_{a+w}=105kg \times v_{a+w}=25\frac{kgm}{s} \\ \frac{25kgm/s }{105kg} =0.2381 \frac{m}{s}$

He will then be moving at 0.2381 m/s in the same direction the wrench was moving initially.