Question

A 50 kg astronaut floating in space throws her 2 kg wrench to the left at 10

Answer 1

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:

$p=mv+MV$ (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:

$0=mv+MV\\V=-\frac{mv}{M}=-\frac{(2)(10)}{50}=-0.4 m/s$

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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