# An astronaut with a mass of #95# #kg# is floating in space. If the astronaut throws an object with a mass of #2# #kg# at a speed of #7/8# #ms^-1#, how much will his speed change by?

The astronaut will have the same momentum in the opposite direction to the thrown object. Given his greater mass, this means his speed will change from

Prior to the object being thrown, the total momentum is zero, and it must remain zero thereafter.

In the opposite direction, the astronaut's momentum will be the same:

Organizing:

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To calculate the change in the astronaut's speed after throwing the object, we can use the principle of conservation of momentum. According to this principle, the total momentum before an event is equal to the total momentum after the event, assuming no external forces act on the system.

The initial momentum of the astronaut-object system is the sum of the momentum of the astronaut and the momentum of the object. Momentum (p) is calculated as mass multiplied by velocity.

The initial momentum of the astronaut-object system is: 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)

Using the conservation of momentum principle, we can set the initial momentum equal to the final momentum and solve for the final velocity of the astronaut.

Initial momentum = Final momentum

(95 kg * 0 m/s) + (2 kg * 7/8 m/s) = (95 kg * final velocity) + (2 kg * 0 m/s)

0 + (14/8) kg*m/s = (95 kg * final velocity) + 0

14/8 kg*m/s = 95 kg * final velocity

final velocity = (14/8) / 95 m/s

final velocity ≈ 0.148 m/s

Therefore, the astronaut's speed changes by approximately 0.148 m/s after throwing the object.

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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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