An astronaut with a mass of #75 kg# is floating in space. If the astronaut throws an object with a mass of #7 kg# at a speed of #1/4 m/s#, how much will his speed change by?
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To find the change in speed of the astronaut after throwing the object, we can use the principle of conservation of momentum. The initial momentum of the astronaut and the object is equal to the final momentum after the throw.
Initial momentum = Final momentum
Initial momentum of the astronaut and the object: = (mass of astronaut × initial speed of astronaut) + (mass of object × initial speed of object) = (75 kg × 0 m/s) + (7 kg × 0.25 m/s) = 0 kg⋅m/s + 1.75 kg⋅m/s = 1.75 kg⋅m/s
Final momentum of the astronaut: = (mass of astronaut + mass of object) × final speed of astronaut = (75 kg + 7 kg) × final speed of astronaut = 82 kg × final speed of astronaut
Since momentum is conserved, we have: Initial momentum = Final momentum 1.75 kg⋅m/s = 82 kg × final speed of astronaut
Solving for the final speed of the astronaut: final speed of astronaut = 1.75 kg⋅m/s ÷ 82 kg final speed of astronaut ≈ 0.021 m/s
Therefore, the astronaut's speed will change by approximately 0.021 m/s after throwing the object.
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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
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