Consider a 130 kg astronaut holding a 30 kg object. Initially, the astronaut has

Question

Consider a 130 kg astronaut holding a 30 kg object. Initially, the astronaut has a velocity of 0 m/s. The astronaut then pushes the heavy object rightward with a velocity of 1.5 m/s.

Although the interaction in the scenario is not a collision, the conservation of momentum still applies. The total momentum of the system (the astronaut and the object) is constant.

1) What is the total momentum of the system?

2) What is the momentum of the astronaut after they push the heavy object?

3) What is the astronaut's velocity after pushing the object?

The answer is in units of meters per second.

Explanation / Answer

1) Momentum = mass x velocity

= (130 + 30 kg) *0m/s

= 0 kg-m/s

2) As the momentum is conserved,

final momentum = initial momentum

=> momentum of astronaut + momentum of the object = 0

=> momentum of astronaut + (30 x 1.5) = 0

=> momentum of astronaut = -45 kg-m/s

3) Let v be the velocity.

We just found out:

momentum of astronaut = -45

=> 130 x v = -45

v = -0.346 m/s (negative sign means to the left)

So the astronaut has a final velocity of 0.346 m/s to the left.

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