Question

An astronaut with a mass of `95 kg` is floating in space. If the astronaut throws an object with a mass of `4 kg` at a speed of `3/4 m/s`, how much will his speed change by?

Answer 1

`v_a^'=-0.032" "m/s`

Explanation:

`m_a:"mass of astronaut"`
`v_a:"velocity of astronaut before event. " v_a=0`
`v_a^'=?" velocity of astronaut after event"`

`m_o:"mass of object "m_o=4 kg`
`v_o:"velocity of object before event "v_o=0`
`v_o^':" velocity of object after event "v_o^'=3/4 m/s`

`P_b=m_a*v_a+m_o*v_o=0`
`P_b:"total momentum before event"`
`"Total momentum before event is zero."`

`P_a=m_a*v_a^'+m_o*v_o^'`
`P_a:"Total momentum after event"`
`P_a=95*v_a^'+4*3/4`

`P_a=95*v_a^'+3`

`"We can write " P_b=P_a" because momentum is conserved."`

`0=95*v_a^'+3`

`95*v_a^'=-3`

`v_a^'=-3/95`

`v_a^'=-0.032" "m/s`