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:
[tex]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}[/tex]
This will be the momentum of the astronaut holding the wrench afterward:
[tex]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} [/tex]
He will then be moving at 0.2381 m/s in the same direction the wrench was moving initially.
