A 83.8 kg astronaut is workingon the engines of a spaceship that is drifting thr

Question

A 83.8 kg astronaut is workingon the engines of a spaceship that is drifting through

space with a constant velocity.The astronaut turns away to look at Earth and severalsec-

onds later is 39.6 m behind theship, at rest relative to the spaceship. The only way tore-

turn to the ship without athruster is to throw a wrench directly away from the ship.The

wrench has a mass of 0.608 kg,and the astronaut throws the wrench with a speed of 17.9m/s.

How long does it take theastronaut to reach the ship?

Answer in units of s.

Explanation / Answer

Using the formula p=mv for momentum, you can calculate the momentumgenerated by throwing the wrench. p = .608 kg * 17.9 m/s = 10.8832 kg*m/s According to Newton's laws momentum is conserved. Therefore, youcan set mass(astronaut)*velocity(astronaut) =mass(wrench)*velocity(wrench). 10.8832 kg*m/s = 83.8 Kg * X X = .1299 m/s Then, solve for time. t = d/v We know distance is 39.6 m, divide that by .1299 and you arrive atyour answer. t = 39.6 m / .1299 m/s t = 304.92 s (Just over 5 minutes)

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