An astronaut is in trouble. He is outside the space shuttle and he is moving awa

Question

An astronaut is in trouble. He is outside the space shuttle and he is moving away from the space shuttle at speed 4.00 m/s. He has a rocket gas tank with to change his velocity. The gas is ejected from the tank at relative speed 103.0 m/s; the remaining mass of gas in the tank is 2.2 kg. The mass of the astronaut is 85.0 kg, and that of the rocket tank is 9.0 kg. If he exhausts all the gas in the tank, what will be his velocity (relative to the space shuttle)? Since the velocity in (a) is still moving away from the space shuttle, the astronaut will be lost unless he can throw the tank away with a high enough speed to recoil toward the shuttle. What minimum final velocity of the tank (relative to the space shuttle) will allow the astronaut to reach the shuttle?

Explanation / Answer

apply coservation of momentum a) 4 * (94 + 2 + 8) = 2 * (-103 + 4) + v*(94+8) v = 6.0196 m/s b) 6.0196 * (94+8) = 8u u = 76.75 m/s

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