Question

An astronaut with a mass of `80 kg` is floating in space. If the astronaut throws a `5 kg` object at a speed of `9 m/s`, how much will his speed change by?

Answer 1

The astronaut moves 0.6 m/s in the direction opposite to that of the object he throws.

Explanation:

We will use the principle of the conservation of momentum. We know that the momentum of the Astronaut/object system will be the same before and after he throws the object. Let's assume he starts from rest.

Known:
`m_A= 80 kg`
`m_O= 5 kg`
`v_{Ai} = 0`
`v_{Oi} = 0`
`v_{Of} = 9 m/s`

Find:
`v_{Af} = ?`

Law of Conservation of momentum:
`p_{Ai} + p_{Oi} = p_{Af}+ p_{Of}`

Where `p_{Ai}` is the initial momentum of the Astronaut, `p_{Af}` is the final momentum of the Astronaut, `p_{Oi}` is the initial momentum of the object, `p_{Of}` is the final momentum of the object.

We also know:
`p = mv`

Where `p` is momentum, `m` is mass and `v` is velocity.

Plug into the top equation and solve for `v_{Af}`.

`p_{Ai} + p_{Oi} = p_{Af}+ p_{Of}`

`m_A v_{Ai} + m_O v_{Oi} = m_A v_{Af}+ m_O v_{Of}`

`m_A v_{Ai} + m_O v_{Oi} - m_O v_{Of} = m_A v_{Af}`

`{m_A v_{Ai} + m_O v_{Oi} - m_O v_{Of}} / m_A= v_{Af}`

Now, let's plug in some numbers:

`v_{Af} = {80 kg * 0 + 5 kg * 0- 5 kg * 9 m/s} / {80 kg}`

`v_{Af} = {- 5 kg * 9 m/s} / {80 kg}`

`v_{Af} = - 0.5625 m/s`

`v_{Af} = - 0.6 m/s`