Question

You have been hired to check the technical correctness of an upcoming made-for-TV murder mystery that takes place in a space shuttle. In one scene, an astronaut's safety line is cut while on a spacewalk. The astronaut, who is 200 meters 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 10-kg tool kit and throws it away with a speed of 8 m/s. In the script, the astronaut, who has a mass of 80 kg without the toolkit, survives, but is this correct?

Answer 1

Answer:

The astronaut who has a mass of 80 kg without the toolkit do survive with 40 seconds of remaining air

Explanation:

Due the astronaut throws the 10-kg tool kit away with a speed of 8 m/s, it gives a momentum equivalent but in the other direction, so $I=mv=(10Kg)(8m/s)=80kg*m/s$, then we can find the speed that the astronaut reaches due to its weight we get, $v=\frac{I}{m} =\frac{80kg*m/s}{80Kg} =1m/s$.

Finally, as the distance to the space shuttle is 200m, the time taken to the astronaut to reach it at the given speed will be $t=\frac{d}{v}=\frac{200m}{1m/s}=200s$, as the remaining air time is 4 min or 240 seconds, The astronaut who has a mass of 80 kg without the toolkit do survive with 40 seconds of remaining air.