Question

An astronaut with a mass of `80 kg` is floating in space. If the astronaut throws an object with a mass of `15 kg` at a speed of `2/5 m/s`, how much will his speed change by?

Answer 1

`v_a^'=-0.93" " m/s`

Explanation:

`m_a:"mass of astronaut"`
`v_a:"velocity of astronaut"`
`m_o:"mass of object"`
`v_o=:velocity of object"`

`Sigma P_b:"total momentum before event"`

`Sigma P_b=m_a*v_a+m_o*v_o`
`Sigma P_b=80*0+15*0=0`

`"Total momentum after event "`

`Sigma P_a=m_a*v_a^'+m_o*v_o^'`
`Sigma P_a=80*v_a^'+cancel(15)*2/cancel(5)`
`Sigma P_a^'=80*v_a+6`

`"Sigma P_b=Sigma P_a`
`0=80*v_a^'+6`

`80*v_a^'=-86`

`v_a^'=-80/86`

`v_a^'=-0.93" " m/s`