The energy the athlete has the use to ride to the summit of the hill is equal to the increase in gravitational potential energy of the athlete:
[tex] \Delta U= mg \Delta h [/tex]
where m is the mass of the athlete, g is the gravitational acceleration and [tex] \Delta h [/tex] is the height of the top of the hill with respect to the ground.
In this problem, [tex] m=70 kg [/tex], [tex] g=9.81 m/s^2 [/tex] and [tex] \Delta h=500 m [/tex], therefore the minimum energy the athlete must use is
[tex] \Delta U=(70 kg)(9.81 m/s^2)(500 m)=3.43 \cdot 10^5 J [/tex]
