Homing pigeons avoid flying over large bodies of water, preferring to fly around them instead. Assume that a pigeon released from a boat 1 mile from the shore of a lake flies 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 needs 10/9 as much energy per mile to fly over water as over land, find the location of point P, which minimizes energy used?

Answer 1

if the distance AP = x, the total distance flown is

d = √(1+x^2) + (2-x) where x<2.

If flying over land requires 1 unit of energy, then the energy cost is

c = 10/9 √(1+x^2) + 1(2-x)

Now just find the minimum of c.

Answer 2

5.6

Answer 3

8.9