Question

A 143 kg astronaut is floating in space. She throws a 0.725 kg wrench forward at 13.8 m/s. What is her recoil velocity? (Answer will be m/s).

Answer 1

Answer: -0.07 m/s

Explanation: the previous answer is close, but they forgot to round it up.

Answer 2

Answer: -0.069 m/s

Step-by-step explanation:

According to the conservation of linear momentum, we have: the following:

`p_(i)=p_(f)` (1)

Where:

`p_(i)=0` is the initial momentum of the astronaut, which is initially at rest

`p_(2)=m_(wrench)V_(wrench)+m_(astronaut)V_(astronaut)` is the final momentum, being
`m_(wrench)=0.725 kg`,
`V_(wrench)=13.8 m/s` and
`m_(astronaut)=143 kg`

Then equation (1) is rewritten as:

`0=m_(wrench)V_(wrench)+m_(astronaut)V_(astronaut)` (2)

Finding te velocity of the astronaut
`V_(astronaut)`:

`V_(astronaut)=-(m_(wrench)V_(wrench))/(m_(astronaut))` (3)

`V_(astronaut)=-((0.725 kg)(13.8 m/s))/(143 kg)` (4)

Hence:

`V_(astronaut)=-0.069 m/s` (5) The negative sign of the velocity indicates it is directed to the left, in the opposite side in which the wrench was thrown.