Physics

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Amy age 8 27kg 127cm
Bruce age 12 41kg 149cm

Both Amy and Bruce are learning gymnastics and having trouble being able to get enough height and time in the air to do a back somersault without the coach spotting them.

The coach gives them homework to just focus on jumping straight up and landing back down. He tells them from a standing position with arms 90 degrees in front of them to bring hands down past their hips as far as they can while squatting until their knees are at a 90 angle and the as they stand up from the squat to bring their hands forward and leap straight into the air trying to touch the ceiling!

1. Calculate the momentum for both Amy and Bruce created by the kinetic and elastic energy of the counter movements before the leap.

2. Calculate Accelleration and apply to F=ma to get the Ground Reaction force

3. If each of them precisely gets to a 90 degree knee flex during squat, and rotate their arms from 90 degrees to 270 degrees then back up to 0 degrees, so their arms are at 270 degrees when knees at 90 degrees and arms return to 90 degrees at point their knees return to 0 degrees, what is the height each can reach and the time in the air before they land.

Assume their height is 1/2 above waist and 1/2 below and their knees are 1/2 of the distance between waist and ground.

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