Answer to Question #81832 in Mechanics | Relativity for Cornelius

Question

I have no idea which category this belongs to here, so here’s the questions
Two 75kg astronauts face each other in the vacuum of interstellar space.one astronaut has a 24kg mass which she throws at 1.5ms-1
Explain why the total momentum of the girl does not change as she throws the mass

At what speed does she recoil back

The other astronaut catches the pack.calculate his speed of recoil

Answer 1

The total momentum of the system (girl + 24 kg mass) is a conserved quantity since it can be changed only under the action of the external force, not by some actions inside the system itself. Thus, if a some mass get momentum

$$p_{pack} = m_{pack}v_{pack}$$

the same momentum is obtained by the girl also:

$$p_{girl} = m_{girl}v_{girl} = p_{pack} \Rightarrow v_{girl} = v_{pack} m_{pack}/m_{girl} = 1.5\times 24/75 = 0.48 m/s.$$

Second austronaut was in rest and got the momentum

$$p_{austro}=m_{austro}v_{austro}=p_{pack}.$$

Thus, his speed will be the same as girl's speed.