# An astronaut with a mass of #110 kg# is floating in space. If the astronaut throws an object with a mass of #9 kg# at a speed of #5/9 m/s#, how much will his speed change by?

Since we are only interested in the change (or difference) between the two speeds, the actual initial and final speeds of the astronaut are irrelevant. For the sake of argument, we can assume that the astronaut's initial speed is zero. After all, it says "floating in space," so perhaps that really means zero.

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To find the change in the astronaut's speed, we can use the principle of conservation of momentum.

Initial momentum of the system (astronaut + object) = Final momentum of the system

( m_{astronaut} \times v_{initial} + m_{object} \times v_{object} = (m_{astronaut} + m_{object}) \times v_{final} )

Substituting the given values:

( 110 \times 0 + 9 \times \frac{5}{9} = (110 + 9) \times v_{final} )

( \frac{45}{9} = 119 \times v_{final} )

( v_{final} = \frac{45}{119} )

Therefore, the astronaut's speed will change by ( \frac{45}{119} ) 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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- An astronaut with a mass of #90 kg# is floating in space. If the astronaut throws a #20 kg# object at a speed of #6/5 m/s#, how much will his speed change by?
- An astronaut with a mass of #100 kg# is floating in space. If the astronaut throws an object with a mass of #2 kg# at a speed of #11/9 m/s#, how much will his speed change by?

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