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 `4 m/s`, how much will his speed change by?

Answer 1

His/her speed decreases by `0.37` meters per second.

Explanation:

Using conservation of momentum, which states that,

`m_1u_1+m_2u_2=m_1v_1+m_2v_2`

where:

• `m_1,m_2` are the masses of the two objects

• `u_1,u_2` are the initial velocities of the two objects

• `v_1,v_2` are the final velocities of the two objects

I will assume that both the astronaut and the object are stationary and have no initial velocity whatsoever.

`:.75 \ "kg"*0 \ "m/s"+7 \ "kg"*0 \ "m/s"=75 \ "kg"*v_1+7 \ "kg"*4 \ "m/s"`

`75 \ "kg"*v_1=-28 \ "kg m/s"`

`v_1=(-28color(red)cancelcolor(black)"kg""m/s")/(75color(red)cancelcolor(black)"kg")`

`~~-0.37 \ "m/s"`

So, the astronaut's velocity will be `0.37 \ "m/s"` opposite to their original direction, or their speed will decrease by `0.37 \ "m/s"`.