An astronaut and her gear have a combined mass of 114 kg. She is initially at rest with respect to the satellite that she is attempting to repair. Then she fires a burst of 18.0 g of a hot gas at 645 m/s. How fast will she be moving after the gas has been fired?Multiple choice question.0.102 m/s322 m/s102 m/s645 m/s
Question
An astronaut and her gear have a combined mass of 114 kg. She is initially at rest with respect to the satellite that she is attempting to repair. Then she fires a burst of 18.0 g of a hot gas at 645 m/s. How fast will she be moving after the gas has been fired?Multiple choice question.0.102 m/s322 m/s102 m/s645 m/s
Solution
This problem can be solved using the principle of conservation of momentum. The total momentum before the gas is fired is equal to the total momentum after the gas is fired.
Before the gas is fired, the total momentum is zero because the astronaut is at rest.
The momentum of the gas is its mass times its velocity. The mass of the gas is 18.0 g, which is 0.018 kg (since 1 kg = 1000 g). The velocity of the gas is 645 m/s. So, the momentum of the gas is (0.018 kg)(645 m/s) = 11.61 kg*m/s.
After the gas is fired, the total momentum is the momentum of the astronaut moving in the opposite direction. Let's denote the velocity of the astronaut as v. So, the momentum of the astronaut is (114 kg)(v).
According to the conservation of momentum, these two momenta are equal:
(114 kg)(v) = 11.61 kg*m/s
Solving for v gives v = 11.61 kg*m/s / 114 kg = 0.102 m/s.
So, the astronaut will be moving at 0.102 m/s after the gas has been fired. The correct answer is 0.102 m/s.
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