Question

If you are an astronaut floating untethered in space (like Sandra Bullock in the movie "Gravity") and you want to move somewhere, one thing you can do is to throw something in the opposite direction. If you (mass = 80 kg) are at rest but want to start moving at 2 m/s to the right, at what speed would you need to throw a 5-kg box to the left in order to accomplish this? [Note: 80 kg is just you, without the box. If you're also holding the 5-kg box, then together your mass is 85 kg.]

Answer 1

Using momentum conservation:

Pi = Pf

initially both box and you are at rest, So

Pi = 0

which means Pf = 0

Pf = m1*v1 + m2v2 = 0

m1v1 = -m2v2

m1 = mass of you = 80 kg

m2 = mass of box = 5 kg

v1 = speed of you = +2 m/sec (+ve sign means towards right)

v2 = speed of box = ?

from above equation

v2 = -m1*v1/m2

Using above values:

v2 = -80*2/5 = -32 m/sec (-ve sign means speed is towards left)

So you need to throw box with 32 m/sec towards the left to achieve required speed.

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