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If you are falling, which scenario will cause the greatest change in momentum when you land?Long time intervalShort time intervalMore information is needed Your change in momentum is the same no matter whatSmall force

Question

If you are falling, which scenario will cause the greatest change in momentum when you land?Long time intervalShort time intervalMore information is needed Your change in momentum is the same no matter whatSmall force

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Solution

The greatest change in momentum when you land from a fall would occur with a short time interval.

Here's why:

Momentum is the product of mass and velocity (p=mv). When you fall and land, your velocity changes from a certain value to zero. This change in velocity (which is your final velocity minus your initial velocity) divided by the time it takes for this change to occur (time interval) is your acceleration (a=Δv/Δt).

According to Newton's second law, force equals mass times acceleration (F=ma). So, the force exerted on you when you land is your mass times your acceleration.

If the time interval is short, the acceleration is greater (because the change in velocity is the same but the time is less). Therefore, the force exerted on you is greater.

Since force is related to the change in momentum (F=Δp/Δt), a greater force means a greater change in momentum. Therefore, a short time interval will cause the greatest change in momentum when you land.

This problem has been solved

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