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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 :

The recoil velocity of the astronaut is -0.070 m/s

Explanation:

We can solve this problem by using the principle of conservation of momentum: in fact, in absence of external forces, the total momentum of the astronaut-wrench system must be conserved.

At the beginning, their total momentum is zero:

[tex]p=0[/tex] (1)

Later, after the astronaut throws the wrench, the total momentum is

[tex]p=mv+MV[/tex] (2)

where

m = 0.725 kg is the mass of the wrench

v = 13.8 m/s is the velocity of the wrench

M = 143 kg is the mass of the astronaut

V is the recoil velocity of the astronaut

Since momentum is conserved, (1) = (2), and so we can find V:

[tex]0=mv+MV\\V=-\frac{mv}{M}=-\frac{(0.725)(13.8)}{143}=-0.070 m/s[/tex]

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