Homing pigeons avoid flying over large bodies of water, preferring to fly around them instead. Assume that a pigeon released from a boat
6
6
miles
miles from the shore of a lake (point B in the figure) 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
12
12 miles from point A, the point on the shore closest to the boat, and if a pigeon needs
four thirds
4
3
as much energy per mile to fly over water as over land, find the location of point P, which minimizes energy used.
2 answers
Fix your post, typing in a normal way, and describe the diagram which we obviously cannot see
If we let x = the distance AP, then the energy used is
z = 4/3 √(x^2+6^2) + 12-x
dz/dx = 4x/(3√(x^2+36)) - 1
so find where dz/dx=0
z = 4/3 √(x^2+6^2) + 12-x
dz/dx = 4x/(3√(x^2+36)) - 1
so find where dz/dx=0