# An astronaut with a mass of #80 kg# is floating in space. If the astronaut throws an object with a mass of #12 kg# at a speed of #2 m/s#, how much will his speed change by?

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To find the change in speed of the astronaut, we can use the principle of conservation of momentum. The total momentum before the object is thrown is equal to the total momentum after the object is thrown.

Before: Total momentum before = (mass of astronaut) * (initial speed of astronaut)

After: Total momentum after = (mass of astronaut + mass of object) * (final speed of astronaut)

Using the conservation of momentum equation: (mass of astronaut) * (initial speed of astronaut) = (mass of astronaut + mass of object) * (final speed of astronaut)

Solving for the final speed of the astronaut: (final speed of astronaut) = ((mass of astronaut) * (initial speed of astronaut)) / (mass of astronaut + mass of object)

Substituting the given values: (final speed of astronaut) = ((80 kg) * (0 m/s)) / (80 kg + 12 kg) (final speed of astronaut) = (0 kg*m/s) / (92 kg) (final speed of astronaut) = 0 m/s

Therefore, the final speed of the astronaut after throwing the object will remain unchanged at 0 m/s.

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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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