Can you power up the hill?

Two champion cyclists, each optimized for a different facet of their sport, will tie if you can stretch the hill just so. - Question: This time, we’ll be looking at a model for a cyclist’s speed $v$ as a function of their pedaling power $P$, their mass $m$, and the ground’s angle of inclination $\theta$: \[v=\frac{P}{m\sin{\theta}+10}\] In cycling, roads are marked with a gradient $g$, which is a…