Question

An astronaut with a mass of `75 kg` is floating in space. If the astronaut throws a `7 kg` object at a speed of `5/4 m/s`, how much will his speed change by?

Answer 1

`vec v_a^'=-0.12" " m/s`

Explanation:

`"momentum before event:"`
`.............................................`

`vec P_a=m_a*vec v_a" momentum of astronaut"`
`vec P_a=75*0=0`

`vec P_o=m_o*vec v_o" momentum of object "`
`vec P_o=7*0=0`

`Sigma P_b=0+0=0" total momentum"`

`"momentum after event:"`
`...........................................`

`P_a^'=m_a*v_a^'`
`vec P_a^'=75*vec v_a^'`

`vec P_o^'=m_o*vec v_o^'`
`vec P_o^'=7*5/4=35/4" " kg*m/s`

`Sigma vec P_a=P_a^'+P_o^'`
`Sigma vec P_a=75*vec v_a^'+35/4`

`"in this event momentum is conserved"`
`...............................................................`

`Sigma vec P_b=Sigma vec P_a`
`0=75*vec v_a^'+35/4`

`75*vec v_a^'=-35/4`

`vec v_a^'=-35/300`

`vec v_a^'=-0.12" " m/s`