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Answer: -0.069 m/s
Explanation:
According to the conservation of linear momentum, we have: the following:
[tex]p_{i}=p_{f}[/tex] (1)
Where:
[tex]p_{i}=0[/tex] is the initial momentum of the astronaut, which is initially at rest
[tex]p_{2}=m_{wrench}V_{wrench}+m_{astronaut}V_{astronaut}[/tex] is the final momentum, being [tex]m_{wrench}=0.725 kg[/tex], [tex]V_{wrench}=13.8 m/s[/tex] and [tex]m_{astronaut}=143 kg[/tex]
Then equation (1) is rewritten as:
[tex]0=m_{wrench}V_{wrench}+m_{astronaut}V_{astronaut}[/tex] (2)
Finding te velocity of the astronaut [tex]V_{astronaut}[/tex]:
[tex]V_{astronaut}=-\frac{m_{wrench}V_{wrench}}{m_{astronaut}}[/tex] (3)
[tex]V_{astronaut}=-\frac{(0.725 kg)(13.8 m/s)}{143 kg}[/tex] (4)
Hence:
[tex]V_{astronaut}=-0.069 m/s[/tex] (5) The negative sign of the velocity indicates it is directed to the left, in the opposite side in which the wrench was thrown.
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Rewritten by : Barada
Answer: -0.07 m/s
Explanation: the previous answer is close, but they forgot to round it up.
