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: -0.069 m/s

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 $V_{astronaut}$:

$V_{astronaut}=-\frac{m_{wrench}V_{wrench}}{m_{astronaut}}$ (3)

$V_{astronaut}=-\frac{(0.725 kg)(13.8 m/s)}{143 kg}$ (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.

Answer 2

Answer: -0.07 m/s

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