A pole vaulter of mass 70 kg can run horizontally with a top speed of 10.0 m/s. The current record height for the pole vault is about 6.2 m. 

(a) For the vaulter to clear this height, approximately how much energy must be stored in the pole just before he leaves the ground? Assume the vaulter’s speed is zero just prior to taking off and that you can treat him as a point particle. 

(b) The energy in part (a) is the maximum energy stored in the pole, so we denote it by PE_max. How does PE_max compare to the maximum kinetic energy KE_run of the pole vaulter before he takes off? 

(c) You should find that PE_max is greater than KE_run, which suggests the vaulter is able to go higher than expected based on our simple analysis. Why does our simple analysis underestimate the maximum height the vaulter can clear? Did we overlook some source of kinetic or potential energy? Is the point particle assumption valid?