A 60kg astronaut becomes separated in space from her spaceship. She is 15.0m away from it and at rest relative

Question

A 60kg astronaut becomes separated in space from her spaceship. She is 15.0m away from it and at rest relative to it. In an effort to get back, she throws a 500g wrench with a speed of 8.0m/s in a direction away from the ship. How long does it take her to get back to the ship?

Answer 1

Gee ...
That looks familiar.
Where did I see it?

One must carry wrenches not calculator's to the outer space. And it must be nice to have anorexic astronauts. I think the suit weighs over 80kg. We have to ask NASA.

Answer 2

First we apply the principle of conservation of momentum to derive the speed of the astronaut after throwing the wrench. If m1 & m2 denote the mass of the astronaut & the wrench, and v1 & v2 denote the speeds of the two, respectively

m1.v1 = m2.v2
v1 = m2.v2/m1 = 0.5*8/60 = 0.0667 m/s

If v1 remains constant then the time t to bring the astronaut back to the spaceship is given by

t = s/v1 = 15/0.0667 = 225 sec or 3.75 min