When a bicyclist is riding at 32 km/h in still air, he experiences a drag force (air resistance) of 25 N.
a) Calculate the magnitude of the drag force, and the component in the direction opposite his motion, if he is riding north at 32 km/h when there is a 32-km/h wind blowing from the east (perpendicular to the road). Do this twice:
i) assuming a linear drag force, and
ii) assuming a quadratic drag force. In both cases, assume that the magnitude of the drag force depends only on the speed of the cyclist relative to the air, and is independent of direction (the "spherical cyclist" approximation).
Caution: first find the magnitude and direction of the velocity of the air relative to the cyclist, then the magnitude of the force, and finally get the component of the force.
b) For each of the three cases above (no wind, wind with linear drag, wind with quadratic drag) calculate the power required to maintain a constant speed.