# An astronaut with a mass of #110 kg# is floating in space. If the astronaut throws a #70 kg# object at a speed of #4 m/s#, how much will his speed change by?

Sum impulses stays constant, or

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To find the change in the astronaut's speed, you can use the principle of conservation of momentum. The initial momentum of the system (astronaut plus object) equals the final momentum. Therefore, the change in the astronaut's speed can be calculated by dividing the momentum of the thrown object by the total mass of the astronaut and the object.

The momentum of the thrown object is its mass multiplied by its velocity. So, ( momentum_{object} = mass_{object} \times velocity_{object} ).

The total initial momentum of the system is the sum of the momentum of the astronaut and the momentum of the object.

( initial , momentum_{total} = mass_{astronaut} \times initial , velocity_{astronaut} + momentum_{object} ).

The final momentum of the system, after the object is thrown, is the sum of the momentum of the astronaut and the momentum of the object.

( final , momentum_{total} = mass_{astronaut} \times final , velocity_{astronaut} + momentum_{object} ).

Since momentum is conserved, ( initial , momentum_{total} = final , momentum_{total} ), so you can solve for the final velocity of the astronaut.

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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.

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