Question

An astronaut with a mass of `90 kg` is floating in space. If the astronaut throws an object with a mass of `5 kg` at a speed of `3/4 m/s`, how much will his speed change by?

Answer 1

`v_a^'=-0.04" "m/s`

Explanation:

`"Before event:"`
`P_a=m_a*v_a`
`P_a:"momentum of astronaut"`
`m_a:"mass of astronaut"`
`v_a:"velocity of astronaut"`
`P_a=90*0=0`

`P_o=m_o*v_o`
`P_o:"momentum of object"`
`m_o:"mass of object"`
`v_o:"velocity of object"`
`P_o=5*0=0`

`P_b=P_a+P_o=0" total momentum"`

`"After event:"`
`P_a'=m_a*v_a'`
`P_a^'=90*v_a^'`

`P_o=m_o*v_o^'`
`P_o=5*3/4=15/4`

`0=90*v_a^'+15/4`

`90*v_a^'=-15/4`

`v_a^'=-15/(90*4)`

`v_a^'=-1/(6*4)=-1/24`

`v_a^'=-0.04" "m/s`