Chapter 6.2, Problem 14E

Pigeon Flight Repeat Exercise 13, but assume a pigeon needs 10/9 as much energy to fly over water as over land.

Pigeon Flight Homing pigeons avoid flying over large bodies of water, preferring to fly around them instead.(One possible explanation is the fact that extra energy is required to fly over water because air pressure drops over water in the daytime.) Assume that a pigeon released from a boat 1 mile from the shore of a lake (point $B$ in the figure) files first to point $P$ on the shore and then along the straight edge of the lake to reach its home at $L$. If $L$ is 2 miles from point $A$, the point on the shore closest to the boat and if a pigeon need 4/3 as much energy per mile to fly over water as over land. Find the location of point $P$, which minimizes energy used.