If there were no air-resistance and the planes' engines were not working, the two planes' velocities at C would be the same; though the average speed along arc ABC would be less than that along arc ADC, since velocity increases with the fall
THE MECHANICS OF LIQUIDS AND GASES 197
and decreases with the rise of the plane, so that the velocity at B is less than at D.
In fact, the plane overcomes drag which is proportional to the square of its velocity, and it is on this that most of the work done by the engine goes. Since the average speed on arc ADC is greater, so also is the work done by the engine to overcome frontal resistance greater on that arc. And if the power developed is the same for both planes, then the kinetic energy of the plane flying along arc ADC, and therefore its velocity, will be less at C than the kinetic energy and velocity of the plane flying along arc ABC.