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.102 m/s645 m/s322 m/s0.102 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.102 m/s645 m/s322 m/s0.102 m/s
Solution
To solve this problem, we need to use 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.
The initial momentum (P_initial) is 0 because the astronaut is at rest.
The final momentum (P_final) is the sum of the momentum of the astronaut and the momentum of the gas.
Momentum is calculated as the product of mass and velocity (p=mv).
First, we need to convert the mass of the gas from grams to kilograms because the mass of the astronaut is given in kilograms.
18.0 g = 0.018 kg
The momentum of the gas is then:
p_gas = m_gas * v_gas = 0.018 kg * 645 m/s = 11.61 kg*m/s
Since the total initial momentum was 0 and momentum is conserved, the final momentum of the astronaut must be equal in magnitude and opposite in direction to the momentum of the gas.
Therefore, the velocity of the astronaut (v_astronaut) can be found by rearranging the momentum equation to solve for velocity:
v_astronaut = p_gas / m_astronaut = 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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