An astronaut of mass 83.0 kg is taking a space walk to work on the International
ID: 1503536 • Letter: A
Question
An astronaut of mass 83.0 kg is taking a space walk to work on the International Space Station. Because of a malfunction with the booster rockets on his spacesuit, he finds himself drifting away from the station with a constant speed of 0.390 m/s. With the booster rockets no longer working, the only way for him to return to the station is to throw the 9.15 kg wrench he is holding. In which direction should he throw the wrench? He throws the wrench with speed 9.82 m/s WITH RESPECT TO HIMSELF. After he throws the wrench, how fast is the astronaut drifting toward the space station? Your response is within 10% of the correct value. This may be due to roundoff error, or you could have a mistake in your calculation. Carry out all intermediate results to at least four-digit accuracy to minimize roundoff error. What is the speed of the wrench with respect to the space station?Explanation / Answer
The person moves one way as the wrench is thrown the other.
the wrench and the person are together we know that the centre of mass is moving at 0.390 m/s relative to the space station.
And that the space station has no forces on it so it remains an inertial frame.
the person moves backwards at - V and the wrench moves forwards at u
We know that u + V = 9.82 ie the relative speed is 9.82
According to conservation of momentum
u*9.15 = V *83
so from these two equations u *9.15 u / 83 = 9.82
u* (1 + 9.15/83) = 9.82
u = 9.82 / (1+ 9.15/83) = 8.8468 m/s from the centre of mass.
and he throws it away from the space station
so its final velocity relative to that station is 0.390 + 8.8468 = 9.2368 m/s
speed with respect to station :-
V *(1 + 83/9.15) = 9.82
V = 9.82 / (1+83/9.15)
V = 0.975 m/s
So his speed relative to the ship becomes
0.975 - 0.390 = 0.585 m/s towards the ship.
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