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 the space shuttle. In one scene, an astronaut's safety line is cut while on a space walk. The astronaut, who is at d=225 m away from the shuttle and not moving with respect to it, finds that the suit's thruster pack has also been damaged and no longer works and that only 4 minutes of air remains. To get back to the shuttle, the astronaut unstraps a tool kit with mass m=10 kg and throws it away with a speed of vT=8 m/s. In the script, the astronaut, who has a mass M=80 kg without the toolkit, survives, but is this correct? Find the time t that he needs to get back to the shuttle.

Explanation / Answer

Before throwing the tool kit the net linear moment, was zero.

According to the law of conservation of linear momentum the net linear momentum after the throw should also be zero.

So, let the velocity of astronaut after the throw be v

Writing the momentum equation,

Mv + mvT = 0

80v + 10x8 = 0

v = -80 / 80 = -1 m/s

-ve sign indicates the direction opposite to the direction of the tool kit which is towards the shuttle.

So, the astronaut is finally moving with a speed of 1 m/s towards the shuttle.

Maximum distance that he can cover in 4 min (240 seconds) is 1 x 240 = 240 m

But the shuttle is at a distance of 225m from him. So, with that speed, he needs only 225 seconds to reach the shuttle, whereas the time he has is 4min. So, he could have survived.

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