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Answer :
Final answer:
To find the capsule's change in speed, apply the conservation of momentum. The astronaut's momentum is set equal to the spacecraft's momentum with opposite sign. The calculated change in speed for the space capsule is roughly 0.160 m/s.
Explanation:
To find the change in speed of the space capsule after the astronaut pushes off, we use the law of conservation of momentum. Before the push, both the astronaut and the space capsule are stationary, so their total momentum is 0. After the astronaut pushes off, the momentum of the astronaut and the capsule must still add up to 0 because momentum is conserved.
The momentum of the astronaut is the product of his mass and velocity, given by 124 kg × 2.20 m/s. The momentum of the space capsule will be the product of its mass and its change in velocity.
By setting the momentum of the astronaut equal and opposite to the momentum of the capsule, you can solve for the capsule's change in speed.
Mathematically:
Momentum of astronaut = -Momentum of capsule
124 kg × 2.20 m/s = 1710 kg × Δv
Δv = (124 kg × 2.20 m/s) / 1710 kg
Δv ≈ 0.160 m/s
Therefore, the space capsule's change in speed is approximately 0.160 m/s.
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