Question: A pigeon is released from a boat (point B in Figure) floating on a lake. Because of falling air over the cool water, the energy required to fly one meter over the lake is twice the corresponding energy e required for flying over the bank (e = 3 joule/meter). To minimize the energy required to fly from B to the loft, L, the pigeon heads to a point P on the bank and then flies along the bank to L. The distance (AL)¯ is 2000 m, and (AB)¯ is 500 m.
(a) Express the energy required to fly from B to L via P as a function of the angle θ (the angle BPA).
(b) What is the optimal angle θ?
(c) Does your answer change if (AL)¯, (AB)¯, and e have different numerical values?
