First, lets find power output of the cyclist when there is no wind:
With the wind blowing we find that the speed of wind which the cyclist feels has value V equal to
and makes an angle a with the vector of cyclist'sdisplacement:
Power output with the wind present is thus
Let me explain a little: the force of the wind is proportional to V^2 but work done is . where is the vector of displacement. Power is therefore:
You are sked to compute . If You do the calculations you'll get required answer Sqrt.