Momentum, Impulse, Collision...?

Question

You have been hired to check the technical correctness of an upcoming TV mystery, Mari Mar in Space. The mystery takes place in the space shuttle. In one scene, the astronaut Mari Mar’s safety line is sabotaged while she is on a space walk, so she is no longer connected to the space shuttle. She checks and finds that her thruster pack has also been damaged and no longer works. She is 200 meters from the shuttle and moving with it. That is, she is not moving with respect to the shuttle. There she is drifting in space with only 4 minutes of air remaining. To get back to the shuttle, she decides to unstrap her 10-kg tool kit and throw it away with all her strength, so that it has speed of 8 m/s. In the script, she survives, but is this correct? Her mass, including space suit, is 80 kg.

Pls show all necessary calculations with explanations pls, best answers gets 10 points...

Answer 1

We are of course assuming this is an ideal and quite hypothetical situation.

Apply conservation of momentum. Meaning that the momentum of Mari Mar must be equal to the momentum of the tossed away stuff.

Momentum of tossed away stuff = mv = 10*8 = 80
Momentum of Mari Mar = 80*V
And 80V = 80 ...... the momentums must be equal
Divide by 80 and get V = 1 m/s

So Mari Mar gives herself a speed of 1 m/s. Since she is 200 meters from the shuttle it should take her 200 seconds or 3 and 1/3 minutes to get back. I think she will make it back OK.