Question

Once​ Kate's kite reaches a height of 52 ft ​(above her​ hands), it rises no higher but drifts due east in a wind blowing 6 ft divided by s. How fast is the string running through​ Kate's hands at the moment that she has released 105 ft of​ string?

Answer 1

5.213ft

Step-by-step explanation:

Z² = x² + y²

x = √(z² - y²)

y = 52ft, dx = 6ft, z = 105ft, dz = ?

d(z² = x² + y²)

2zdz = 2xdx

dz = xdx/z

But x = √(z² - y²)

dz = √(z² - y²)/z * dx

dz = [√(105² - 52²)/105] * 6

dz = √(8521)/ 17.5

dz = 5.213ft