Question

An astronaut with a mass of `110 kg` is floating in space. If the astronaut throws an object with a mass of `9 kg` at a speed of `5/9 m/s`, how much will his speed change by?

Answer 1

`1/22` m/s

Explanation:

Quantities:
`m_a = 110` kg
`m_o = 9` kg
`v_(o_f) = 5/9` m/s
`v_(a_f) = ?` m/s
`v_(a_i) = v_(o_i) \equiv v_i` m/s

`p_(a_i) + p_(o_i) = p_(a_f) + p_(o_f)`

`m_av_(a_i) +m_ov_(o_i) = m_av_(a_f) + m_ov_(o_f)`

`(m_a + m_o)v_i = m_av_(a_f) + m_ov_(o_f)`

`(110 + 9)v_i = (110)v_(a_f) + (9)(5/9)`

`119v_i = 110v_(a_f) + 5`

We can assume that the initial speed of the astronaut is zero for the sake of argument. It says "floating in space", so maybe that actually means 0. The actual initial and final speeds are unimportant, because we are just looking for the change (or difference) in the two speeds.

`-5 = 110v_(a_f)`

`v_(a_f) = -1/22`

This means that the astronauts speed will change by `1/22` m/s and the astronaut will move in the opposite direction of the object (hence the minus sign).