PS7 - If the cyclist starts coasting at the bottom of the hill, what distance, in meters, does the bike travel up the incline?

Question

A cyclist, starting from rest, applies a horizontal force of F = 317 N to his bicycle, moving across flat ground for a distance of d_flat = 283 m before encountering a hill making an angle of θ = 19.6° with respect to the horizontal. The bicycle and rider have a combined mass of m = 128.9 kg. Ignore air resistance and other losses due to friction. The rider does about 89,711 J of work before reaching the hill (W = 89,711 J). To add, the bicycle's speed, just before reaching the hill is about v = 37.31 m/s.

Answer 1

Kinetic energy at bottom of hill is 0.5mv^2 = 0.5 x 128.9 x 37.31 x 37.31 (lets call this KE)

This will be completely converted to GPE when the cyclist stops up the incline

So if h is the vertical distance from the ground to the stopping point mgh = KE

m = 128.9, g = 9.8, so you can calculate h

If l is the distance up the incline then using trig, h/l = sin 19.6, so knowing h, you can calculate l.