The astronaut will move at 0.4 m/s in the opposite direction to the wrench
Explanation:
We can solve this problem by using the law of conservation of momentum. In fact, the total momentum of the astronaut-wrench system must be conserved before and after the launch.
Before the launch, the total momentum is zero, since the astronaut is at rest:
p = 0 (1)
After the launch, the total momentum is:
[tex]p=mv+MV[/tex] (2)
where :
m = 2 kg is the mass of the wrench
v = 10 m/s is the velocity of the wrench
M = 50 kg is the mass of the astronaut
V is the recoil velocity of the astronaut
Since momentum is conserved, we can write (1) = (2), and so we can solve for V:
[tex]0=mv+MV\\V=-\frac{mv}{M}=-\frac{(2)(10)}{50}=-0.4 m/s[/tex]
And the negative sign means that the astronaut will move in the opposite direction to the wrench.
Learn more about conservation of momentum:
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