# An astronaut with a mass of #95 kg# is floating in space. If the astronaut throws an object with a mass of #3 kg# at a speed of #1/8 m/s#, how much will his speed change by?

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To find the change in velocity of the astronaut, we can use the principle of conservation of momentum. The initial momentum of the system (astronaut plus object) is equal to the final momentum of the system.

Initial momentum = (mass of astronaut * initial velocity of astronaut) + (mass of object * initial velocity of object)

Final momentum = (mass of astronaut * final velocity of astronaut) + (mass of object * final velocity of object)

Since the astronaut is initially at rest, the initial velocity of the astronaut is 0 m/s. The initial momentum of the system is therefore equal to the momentum of the object.

Initial momentum = mass of object * initial velocity of object = 3 kg * (1/8 m/s) = 3/8 kg*m/s

Final momentum = (mass of astronaut * final velocity of astronaut) + (mass of object * final velocity of object) = (95 kg * vf) + (3 kg * 0 m/s) (since the object is no longer in contact with the astronaut, its final velocity is 0 m/s) = 95 kg * vf

According to the principle of conservation of momentum, initial momentum = final momentum:

3/8 kg*m/s = 95 kg * vf

Solving for vf:

vf = (3/8 kg*m/s) / 95 kg = 3/760 m/s

Therefore, the astronaut's velocity changes by 3/760 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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