The change in potential energy of the bike racer is equal to
[tex]\Delta U = mg\Delta h[/tex]
where m is the mass of the bike racer, [tex]g=9.81 m/s^2[/tex] and [tex]\Delta h[/tex] is the change in altitude of the racer. This [tex]\Delta h[/tex] corresponds to the height of the ramp, which is [tex]L=1500 m[/tex] long. Therefore the height of the ramp (and the variation of altitude) is
[tex]\Delta h=L \sin (4.3^{\circ})=112.5 m[/tex]
And so, the variation of potential energy of the racer is
[tex]\Delta U = mg\Delta h=(76 kg)(9.81 m/s^2)(112.5m)=8.39 \cdot 10^4 J[/tex]
