# An astronaut with a mass of #75 kg# is floating in space. If the astronaut throws a #4 kg# object at a speed of #6 m/s#, how much will his speed change by?

Since there is no force acting on the system due to the astronaut's floating in space, the total momentum is conserved.

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To calculate the change in the astronaut's speed when throwing the object, we can use the principle of conservation of momentum.

First, we calculate the initial momentum of the system (astronaut plus object) before the throw:

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

Initial momentum = (75 kg * 0 m/s) + (4 kg * 6 m/s)
= 0 kg*m/s + 24 kg*m/s
= 24 kg*m/s

Then, we calculate the final momentum of the system after the throw. Since the astronaut and the object are now separate, the final momentum is only due to the astronaut's new speed:

Final momentum = mass of astronaut * final speed of astronaut

Final momentum = 75 kg * final speed of astronaut

To find the final speed of the astronaut, we equate the initial and final momentums:

Initial momentum = Final momentum

24 kg*m/s = 75 kg * final speed of astronaut

Solving for the final speed of the astronaut:

final speed of astronaut = 24 kg*m/s / 75 kg ≈ 0.32 m/s

Therefore, the astronaut's speed will change by approximately 0.32 m/s after throwing the object.

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The astronaut's speed will change by approximately -0.32 m/s. This is calculated using the principle of conservation of momentum, where the change in momentum of the astronaut and the object is equal and opposite. The change in momentum of the object is (4 , \text{kg} \times 6 , \text{m/s} = 24 , \text{kg} \cdot \text{m/s}). Since the astronaut's initial momentum is zero, the change in momentum of the astronaut is -24 kg·m/s. Dividing this by the astronaut's mass (75 kg) gives the change in velocity: (-24 , \text{kg}\cdot\text{m/s} / 75 , \text{kg} ≈ -0.32 , \text{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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