A 68.5-kg astronaut is doing a repair in space on the orbiting space station. She throws a 2.25-kg tool away from her at 3.20 m>s relative to the space station. With what speed and in what direction will she begin to move?

She'll move with a speed of 0.105 m/s In the direction opposite the direction in which she threw the tool.

Explanation:

The momentum of the two bodies is conserved according to Newton's second law of motion.

Total Momentum in before throwing the tool = total momentum of the tool + astronaut after throwing the tool

Since they both aren't moving before throwing the tool, momentum before throwing the tool = 0 kgm/s

Momentum of tool after being thrown = mv = 2.25 * 3.2 = 7.2 kgm/s

Momentum of astronaut after throwing the tool = mv = 68.5 * v = 68.5v kgm/s

0 = 7.2 + 68.5v

68.5 v = - 7.2

v = - 7.2/68.5 = - 0.105 m/s

This means she'll move with a speed of 0.105 m/s In the direction opposite the direction in which she threw the tool.