Related Rates Question

Question

a child flies a kite at a height of 40 feet, the wind is carrying the kite horizontally away from the child at a rate of 25 feet/second. How fast is the length of the string changing when the string that the child let out is 50 feet long?

Answer 1

Draw a right triangle with vertical leg 40, horizontal leg x, and hypotenuse y.

Given: dx/dt = 25

Find: dy/dt when y = 50

Solution:

x² + 40² = y² When y = 50, x² = 50² - 40² = 900. So, x = 30.

2x(dx/dt) = 2y(dy/dt)

dy/dt = x(dx/dt) / y = 30(25) / 50 = 15 ft/sec