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A circus acrobat of mass M leaps straight up with initial velocity $v_0$ from a trampoline. As he rises up, he takes a trained monkey of mass m off a perch at a height h above the trampoline. What is the maximum height attained by the pair?

The only thing I don't understand is why the vertical momentum is conserved when the acrobat catches the monkey despite the presence of gravitational force?

That's the only part in the solution where the conservation of momentum will be used to find the final velocity of acrobat and monkey.

I guessed that it must be because of normal force balancing the gravitational force out but am not sure of it.

tom
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suiz
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1 Answers1

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Gravity is a distraction here.

The acrobat will be slowing down as (s)he goes up due to gravity, but what we care about is that at the moment the monkey is taken the acrobat and the monkey are together - we combine their masses and use conservation of momentum to find the new upwards velocity.

Often momentum questions are in horizontal planes to avoid gravity, $e.g.$ train on a flat straight track.

Here you need to use gravity to find the velocity at the pick up point, linear momentum conservation to find the new velocity after pick up and then gravity to find how high the pair go with their new velocity.

I thnk the easiest way to understand this is to consider that the pickup takes place in such a sort period of time that the change of velocity due to gravity is negligible.

Hope this helps.

tom
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