Answer :
Final answer:
The astronaut's velocity after being hit by a piece of debris bounces off in space is approximately 0.365 m/s, calculated using conservation of momentum.
Explanation:
The question involves a physical interaction in space where conservation of momentum should be applied to find the velocity of the astronaut after being hit and bounces off a piece of debris. To find the astronaut's velocity after the collision, we use the conservation of momentum principle, which states that the total momentum before the collision is equal to the total momentum after the collision.
The initial momentum of the astronaut is zero because the astronaut is at rest. The momentum of the debris before the collision can be calculated using the formula:
p = mv
where p is momentum, m is mass, and v is velocity.
For the debris:
pdebris initial = 0.035 kg * 875 m/s
For the astronaut after being hit, considering the astronaut and debris system isolated:
(84 kg * vastronaut final) + (0.035 kg * -5 m/s) = 0.035 kg * 875 m/s
Solving for vastronaut final:
vastronaut final = (0.035 kg * 875 m/s + 0.035 kg * 5 m/s) / 84 kg ≈ 0.365 m/s
Hence, the astronaut's velocity after being hit by the debris is approximately 0.365 m/s.
