Springs, Hooke's Law, Work, and Energy

[x2022]

Homework Statement

The above image shows Yelena Isinbayeva (69.5 kg) at a point in her vault where the pole is maximally deflected (Δx = 1.41 m). The pole has a bending stiffness of 1158 N/m and behaves according to Hooke's Law. At this point in the vault, her vertical velocity is 4.33 m/s and she is 2.92 m above the ground.

If all of the stored stain energy is transferred from the pole to the vaulter, then what will be the peak height of her center of mass (relative to the ground) during the vault?

Relevant Equations

Stored Stain energy stored in pole = 1151.11
Work done by pole = 1151.11
Force applied to pole = 1632.78
Kinetic energy in Y = 651.52
Gravitational Kinetic Energy = 1990.84

The formulas we have been given include Potential energy=mgh, Stored strain energy=(1/2)K(change in X)^2, , Kinetic energy=(1/2)mV^2, Work=F(change in d), Force=K(change in X). Not sure how exactly to answer the question.

 

[haruspex]

Homework Statement: The above image shows Yelena Isinbayeva (69.5 kg) at a point in her vault where the pole is maximally deflected (Δx = 1.41 m). The pole has a bending stiffness of 1158 N/m and behaves according to Hooke's Law. At this point in the vault, her vertical velocity is 4.33 m/s and she is 2.92 m above the ground.

If all of the stored stain energy is transferred from the pole to the vaulter, then what will be the peak height of her center of mass (relative to the ground) during the vault?
Homework Equations: Stored Stain energy stored in pole = 1151.11
Work done by pole = 1151.11
Force applied to pole = 1632.78
Kinetic energy in Y = 651.52
Gravitational Kinetic Energy = 1990.84

The formulas we have been given include Potential energy=mgh, Stored strain energy=(1/2)K(change in X)^2, , Kinetic energy=(1/2)mV^2, Work=F(change in d), Force=K(change in X). Not sure how exactly to answer the question.

You have found all the components of her mechanical energy at the point in the (missing) diagram.
What will be the components of her mechanical energy at the peak of her trajectory?