In this example we will consider conservation of momentum in an isolated system

Question

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? What is the magnitude of her recoil velocity if she throws the wrench at 10 m/s? Will her recoil velocity be great enough to get her back to the spacecraft before she runs out of air?If the astronaut has only a 6 minute air supply left, how fast must she throw the wrench so that she makes it back to the spaceship in time?

Explanation / Answer

Using momentum conservation

(100) V = (1kg) (10)

V = 0.1 m/s

Speed is distance over time

V = d/t or

t = d /V = `1000m/0.1 m/s = 1000s

Time to reach the spaceship 1000s but astronaut has 1200 s ( 20 min * 60 s). She is safe.

b)

If she has 6 min which mean 360s then speed needed is

V = d /t = 1000/360 = 2.788m/s

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