Why it's hard to go fast

Bicyclists and other things that go fast must overcome air resistance, or drag, even to maintain a constant speed. A simple empirical model for the drag force on an object when the air flows smoothly around the object is FDrag=cv\vec{F}_{Drag}=-c\vec{v}, where v\vec{v} is the velocity of the object and cc is a constant that depends on the size and shape of the object. Consider a bicyclist putting out some power P0P_0 (in watts) to overcome drag and maintain some constant speed v0v_0. She then increases her speed to 1.2v01.2 v_0, which requires her to put out a power P1P_1 to maintain. What is the ratio P1P0\frac{P_1}{P_0}?

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