# An astronaut with a mass of #95 kg# is floating in space. If the astronaut throws an object with a mass of #4 kg# at a speed of #1/8 m/s#, how much will his speed change by?

This examines momentum conservation.

It is assumed that there is no air resistance and no gravity because the astronaut is floating in space, so you should move backward when you toss an object forward.

Newton's Third Law states that an object will push you back if you push it. Since the astronaut and the object are moving in different directions, if the object is thrown to the right, we have conservation of momentum in the following way:

Consequently:

The astronaut's new speed is represented by the change in speed, assuming that he began at rest.

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To find the change in the astronaut's speed, you can use the principle of conservation of momentum. The change in momentum of the astronaut and the object will be equal and opposite. Calculate the initial momentum of the astronaut and the object, then calculate the final momentum after the object is thrown. Finally, use the equation Δp = mΔv to find the change in 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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