(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A cyclist develops constant power when cycling. The air resistance is proportional to the speed of cycling. When he cycles on level ground, the maximum velocity he can attain is v. When he cycles up a slope, his maximum velocity is 1/2v. If he cycles down the same slope, his maximum velocity is av. Ask what is the value of a.

2. Relevant equations

3. The attempt at a solution

The cyclist exerts the same amount of force on the bike at all velocity,thus

On level ground: F = kv_{2}

cycling up a slope: F = 1/4kv^{2}+ mgsinθ

kv^{2}= 1/4kv^{2}+ mgsinθ

mgsinθ = 3/4kv^{2}

cycling down the slope: kv^{2}+ 3/4kv^{2}= k(av)^{2}

a^{2}= 7/4

a = (7/4)^{1/2}

But this is not the correct answer. Can anyone tell me where did I go wrong?

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# Homework Help: Work, Energy and Power question

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