Question #288113

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?

Expert's answer

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}\\\\\n=\\frac{746}{58*9.8\\sin16^\\circ}=4.8\\:\\rm m\/s"

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