Question

How fast must a 58 kg mountaineer climb a hill that has a slope of 16° to come up with a power output of 1.0 hp?

Answer 1

Given:

$m=58\:\rm kg$

$\theta=16^\circ$

$P=1.0\rm \: hp=746\: W$

The power is related to the speed and force by an equation

$$P=Fv=mg\sin\theta v$$

Hence, the speed of a mountaineer

$$v=\frac{P}{mg\sin\theta}\\ =\frac{746}{58*9.8\sin16^\circ}=4.8\:\rm m/s$$