Question

Homing pigeons avoid flying over water. Suppose a homing pigeon is released on an island at point c, which is 10 mi directly out in the water from a point b on shore. Point b is 22 mi downshore from the pigeon's home loft at point a assume that a pigeon flying over water uses energy at a rate 1.28 times the rate over land. Toward what point s downshore from a should the pigeon fly in order to minimize the total energy required to get to the home loft at a?

Answer 1

$<b>$
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

Explanation:

<b>

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.