Question

An astronaut with a mass of `90 kg` is floating in space. If the astronaut throws an object with a mass of `7 kg` at a speed of `2/9 m/s`, how much will his speed change by?

Answer 1

`"the change of speed of astronaut is :" v_a=-0.02 m/s`

Explanation:

`m_a:90 kg" mass of astronaut "`
`m_o:7 kg" mass of object"`

`"let total momentum before thrown the object be "Sigma P_b`

`v_a:0" speed of astronaut"`
`v_o:0" speed of object"`

`Sigma P_b=m_a*v_a +m_o*v_0`
`v_a=0" , "v_o=0`
`Sigma P_b=90*0+7*0=0`

`"let total momentum after thrown the object be "Sigma P_a`

`u_a:?"speed of astronaut after thrown the object"`
`u_o:2/9 m/s" speed of object thrown."`

`Sigma P_a=m_a*u_a+m_o*u_o`
`Sigma P_a=90*u_a+7*2/9`
`Sigma P_a=90*u_a+14/9`

`"According to the principle of momentum conservation, the total"` `"momentum before the object is thrown is equal to the total"` `"momentum after the object is thrown."`

`Sigma P_b=Sigma P_a`
`0=90*u_a+14/9`
`90*u_a=-14/9`
`u_a=-14/(90*9)`
`u_a=-14/810`
`u_a=-0.02 m/s" rounded the two decimal place."`

`"Minus sign tells us that the direction of the speed of astronaut "`
`"is opposite to the direction of the speed of object."`