Question

An astronaut with a mass of `85 kg` is floating in space. If the astronaut throws an object with a mass of `5 kg` at a speed of `1/4 m/s`, how much will his speed change by?

Answer 1

`v_a^'=-0.015" " m/s`

Explanation:

`m_a=85 " "kg " mass of astronaut"`

`v_a=0" velocity of astronaut before event"`

`P_a=m_a*v_a=85*0=0" momentum of astronaut before event"`

`m_o=5" "kg`

`v_o=0" velocity of object before event"`

`P_o=m_o*v_o=5*0=0" momentum of object before event"`

`P_i=P_a+P_o" "P_i=0 " total momentum before event"`

`v_a^'="velocity of astronaut after event"`

`P_a^'=m_a*v_a^'=85*v_a^'" momentum of astronaut after event"`

`P_o^'=m_o*v_o^'=5*1/4=5/4 kg*m/s" object's momentum after event"`

`P_f=P_a^'+P_o^'`

`P_f=85*v_a^'+5/4" total momentum after event"`

`P_i=P_a`

`0=85*v_a^'+5/4`

`85*v_a^'=-5/4`

`v_a^'=-5/(85*4)`

`v_a^'=-0.015" " m/s`