# An astronaut with a mass of #90 kg# is floating in space. If the astronaut throws an object with a mass of #3 kg# at a speed of #2 m/s#, how much will his speed change by?

Sol:-

The astronaut's momentum and the object's momentum must coincide.

v_1=(3*2)/90=6/90=2/30=0.067 m/s is implied by this.

suggests that v_1=0.067m/s.

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To find the change in speed of the astronaut after throwing the object, you can use the principle of conservation of momentum. The initial momentum of the astronaut-object system is equal to the final momentum of the astronaut-object system.

Initial momentum = Final momentum (90 kg) * (initial speed of astronaut) = (90 kg + 3 kg) * (final speed of astronaut)

Solving for the final speed of the astronaut:

90 kg * initial speed of astronaut = (90 kg + 3 kg) * final speed of astronaut 90 kg * initial speed of astronaut = 93 kg * final speed of astronaut Initial speed of astronaut = (93 kg * final speed of astronaut) / 90 kg

Substitute the given values:

90 kg * initial speed of astronaut = 93 kg * final speed of astronaut 90 kg * initial speed of astronaut = 93 kg * (initial speed of astronaut + change in speed) 90 kg * initial speed of astronaut = 93 kg * (initial speed of astronaut + Δv)

Rearrange the equation to solve for Δv:

90 kg * initial speed of astronaut = 93 kg * (initial speed of astronaut + Δv) 90 kg * initial speed of astronaut = 93 kg * initial speed of astronaut + 93 kg * Δv 90 kg * initial speed of astronaut - 93 kg * initial speed of astronaut = 93 kg * Δv -3 kg * initial speed of astronaut = 93 kg * Δv Δv = (-3 kg * initial speed of astronaut) / 93 kg

Substitute the given values:

Δv = (-3 kg * 2 m/s) / 93 kg Δv ≈ -0.0645 m/s

Therefore, the astronaut's speed will decrease by approximately 0.0645 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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