In this example, we will consider conservation of momentum in an isolated system consisting of an astronaut and a wrench. An astronaut is floating in space 100 m from her ship when her safety cable becomes unlatched. She and the ship are motionless relative to each other. The astronaut's mass (including space suit) is 100 kg; she has a 1.0 kg wrench and only a 20 minute air supply. Thinking back to her physics classes, she devises a plan to use conservation of momentum to get back to the ship safely by throwing the wrench away from her. In what direction should she throw the wrench

She must throw it in the opposite direction away from herself and the ship. To find the velocity with which she throws it, we consider the law of conservation of momentum.

Since initial momentum = final momentum and the initial momentum of the astronaut and wrench = 0

0 = final momentum

0 = mv + MV where m = mass of wrench = 1.0 kg, v = velocity of wrench, M = mass of astronaut + suit = 100 kg and V = velocity of astronaut.

So. mv = -MV

v = -MV/m

Now, if the astronaut is supposed to cover a distance of 100 m from the space ship in 20 minutes, her velocity should be, V = distance/time = 100 m/ 20 min = 100 m/(20 × 60 s) = 100 m/1200 = 0.0833 m/s

So v = -MV/m

= -100 kg × 0.0833 m/s ÷ 1.0 kg

= -8.33 m/s

She must throw the wrench in the opposite direction away from herself and the ship at a velocity of -8.33 m/s.