You have been hired to check the technical correctness of an upcoming made-for-T

Question

You have been hired to check the technical correctness of an upcoming made-for-TV murder mystery that takes place in space. In one scene, a brave astronaut is out on an emergency spacewalk without a tether to rescue a fellow astronaut. She is 113 m away from her spaceship (and not moving relative to it) when a 9.8-kg piece of space debris moving at 6.2 m/s towards her hits her backpack and becomes embedded in it. The thrusters in the backpack are damaged and she only has 3 minutes and 50 seconds of air left (just the right amount of time for a flashback, of course). Fortunately, the impact pushes her directly towards the spaceship. Does she have enough air to survive? The total mass of the astronaut and space suit is 90 kg.

Explanation / Answer

applying momentum conservation for the collision,

(9.8 x 6.2) + (90 x 0) = (90 + 9.8) v

v = 0.609 m/s

time = d / v = 113 / 0.609

t = 185.6 sec Or 3.09 min

t = 3 min 5.6 sec

Yes, She have enough air to survive.

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