Assuming that the astronaut starts from rest, find the final speed of the astronaut after throwing the tank.?

Question

A 63.0kg astronaut is on a space walk when the tether line to the shuttle breaks. The astronaut is able to throw a 10.0kg oxygen tank in a direction away from the shuttle with a speed of 12.0m/s, propelling the astronaut back to the shuttle.

Answer 1

The probable reason you haven't received an answer so far is that you haven't defined the problem carefully enough.

Is the speed of the oxygen tank (12.0m/s) measured with respect to the shuttle, or to the astronaut? It makes a DIFFERENCE!

I'll work both problems. All momentum will be measured relative to the shuttle:

1.) The tank's 12.0m/s is w.r.t. the shuttle.

To begin with, there is zero momentum relative to the shuttle. Then after the throw, the astronaut has momentum equal but opposite to that of the oxygen tank, 10.0(12.0)kg m/s = 120kg m/s.

Let the astronaut's speed be v; then

(63.0kg) v = 120kg m/s, so that v = 1.9048... m/s.

2.) The tank's 12.0m/s is w.r.t. the astronaut.

Let the astronaut's speed again be represented by v; but now, however, the tank's momentum relative to the shuttle is

10.0 (12.0 - v) kg m/s.

So we now have:

(63.0kg) v m/s = (10.0kg) (12.0 - v) m/s.

Therefore(73.0kg) v m/s = (10.0kg) 12.0 m/s, or v = 1.6438... m/s.

Live long and prosper.