anne and bobby are twins who have the same weight.anne drops straight down to the ground from up in a tree in santa clara.at the same time that anne drops, bobby begins his descent down a nearby frictionless slide. if they start so that their centers of mass are at the same height above the ground, how do their kinetic energies compare when they hit the ground?

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18-11-2022
Physics

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anne and bobby are twins who have the same weight.anne drops straight down to the ground from up in a tree in santa clara.at the same time that anne drops, bobby begins his descent down a nearby frictionless slide. if they start so that their centers of mass are at the same height above the ground, how do their kinetic energies compare when they hit the ground?

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Qwbox Qwbox · Answer 1 · 2022-11-22T19:06:45+01:00

Both Anne and Bobby will have same kinetic energies when they will hit the ground.

In order to answer this question, let us consider a general body of mass M which is released from the height H.

Let us say that the body achieved a speed V when it came to the bottom.

So, law of conservation of energy,

Potential energy at top = kinetic energy at bottom

MgH = 1/2MV²

As we can see from the above relation that the kinetic energy of the body depends only on the height of the body from the ground and the mass of the body.

So if Anne and Bobby both have the same weight and the position of the center of mass of both of them is at a same height from the ground then there kinetic energies will be same in magnitude when the hit the ground.

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