Derive an equation for the velocity of the pole vaulter just before impacting into the pads in terms of initial velocity $(v_i),$ acceleration of gravity $(g),$ and the height of the pads $(h_p).$

Derive an equation for the pole vaulters displacement into the pads in terms of $h_{\text{m}\text{a}\text{x}},m,v_i,g,h_p,$ and $k($you do not have to solve it in all of these terms, but at least some of these terms should be included$).$

The average pole vaulter with a mass of $75kg$ can run up to a velocity of $7\mathrm{.}48\frac{m}{s}.$ The pole vault pads are $0\mathrm{.}81m$ thick and have a spring constant $k=10,000\frac{N}{m}.$ Use the equations you derived previously where necessary to determine and prove if the pole vaulter hits the ground through the pads?