a kite at a height of 60 ft is moving horizontally at a rate of 5 ft/sec away from the boy who flies it. how fast is the cord being released when 100 ft are out?

Answer 1

the length z of cord is

z^2 = x^2 + 60^2
z dz/dt = x dx/dt
when z=100, x=80, so
100 dz/dt = 80 * 5
dz/dt = 4

Answer 2

(100)^2 -(60)^2 = sqrt 6,400 = 80 / 5 = 16

The kite has moved 80 feet away in 16 seconds

The cord has increased 40 feet in 16 seconds (100 -60)

The cord has increased in length at a rate of 40 / 16 = 2.5 feet per second