Vault displays so many aspects of physics..

The Run The gymnast begins her vault with her approach, or her run.  Her run is her Kinetic Energy, KE=1/2mv2

A 50 kg gymnast's Kinetic Energy during her run would normally be:




The Takeoff The gymnast jumps off the springboard, adding more energy to her vault through elastic potential energy.  The gymnast also has angular momentum, which is dependent on the force of the gymnast's muscles, jumping on the board.  PE=1/2kx2



So far, the gymnast has her energy from her run and bouncing off the springboard to complete her vault.

The Flight Off The last part of the vault follows a path of projectile motion. The hips of the gymnast are the her center of mass.  At the top of the flip off the vault, the velocity of the gymnast in the y-direction is zero, so all of the velocity is in the x-direction (which is her initial velocity coming of the vault).  The gymnast's resultant velocity is tangent to the parabola at each point, shown by the diagram below.

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