Question

An astronaut with a mass of `75 kg` is floating in space. If the astronaut throws an object with a mass of `12 kg` at a speed of `5/8 m/s`, how much will his speed change by?

Answer 1

Law of conservation of momentum states
Initial Momentum `=` Final Momentum
We need to remember that both momentum and velocity are vector quantities.
It is assumed that astronaut is holding the thrown object in hand

Let velocity of astronaut before he throws the object be `v_i`

Therefore initial momentum `=(75+12)v_i`
Let final velocity of astronaut`=v_f`
After throwing the object Final momentum`=75v_f+12xx5/8`
Equating the two we obtain
`(75+12)v_i=75v_f+7.5`
Rearranging we obtain
`75(v_f-v_i)=12v_i-7.5`
Change in the velocity of astronaut
`(v_f-v_i)=(12v_i-7.5)/75ms^-1`