Question

a kite is a 150 feet high and 200 feet of string are out. if the kite starts drifting away horizontally at the rate of 4 miles an hour how fast is a string being paid out at the start​

Answer 1

Let z = 200 ft and y = 150 ft

Also since 60 mph = 88 ft/sec then 4 mph = 88/15 = 5.87 ft.sec

Now x^2 + y^2 = z^2

x dx/dt + y dy/dt = z dz/dt differentiate wrt t

Or x dx/dt = z dz/dt since dy/dt = zero

x = (200^2 - 150^2)^1/2 = 132.3 ft

dz/dt = x / z * dx/dt = 132.3 / 200 * 5.87 = 3.88 ft/sec