A cyclist with a mass m=\SI100kg rides without pedaling down a hill with an angle of inclination of θ1=\ang4.8 (angle between the horizontal and the hill) and notices that if the hill is long enough his final speed would be v1=\SI50km/h. However, if the mountain is two times smaller (θ2=\ang2.4) his final speed would be smaller by Δv=\SI15km/h. Find how big must be the cyclist pedaling power so he would maintain a speed of v=\SI20km/h. on a horizontal road. What fraction of the power does it take to overcome the air resistance? Assume that there is a windless weather and that the gravitational acceleration is g=\SI9.8m/s2.
Note. You should take into account the friction force that does not depend on the speed and also the wind resistance which is proportional to speed squared.