Question

An astronaut with a mass of `85 kg` is floating in space. If the astronaut throws a `5 kg` object at a speed of `2/3 m/s`, how much will his speed change by?

Answer 1

Since he was initially at rest, his speed change and final speed are the same: -0.039 m/s.

Explanation:

System momentum is conserved.

`"Momentum before = momentum after"`

`(m_1+m_2)*u = m_1*v_1 + m_2*v_2`

`(85 "kg" + 5 "kg")*0 = 85 "kg"*v_1 + 5 "kg"*2/3 m/s`

`85 "kg"*v_1 = -5 "kg"*2/3 m/s`

`v_1 = (-5 cancel("kg")*2/3 m/s)/(85 cancel("kg")) = -0.039 m/s`

Note: Forgetting that he originally had that 5 kg object with him is not a problem in this case because original velocity was zero. But if he had originally been moving, the original mass of 90 kg would have been a factor.

I hope this helps,
Steve