Question

A man flies a kite at a height of 15 ft. The wind is carrying the kite horizontally from the man at a rate of 5 ft./s. How fast must he let out the string when the kite is flying on 32 ft. of string?

Answer 1

4.4 ft/s

Explanation:

Height = 15ft

Rate= 5 ft/s

Distance from the man to the kite= 32ft

dh/dt = 5 ft/s

h = √32^2 - 15^2

h = √ 1025 - 225

h = √800

h = 28.28ft

D = √15^2 + h^2

dD/dt = 1/2(15^2 + h^2)^-1/2 (2h) dh/dt

= h(225 + h^2)^-1/2 dh/dt

= (h / √225 + h^2)5

= (28.28 / √225 + 28.28^2)5

= (28.28 / √1024.7584)5

= (28.28/32)5

= 0.88*5

= 4.4 ft/s