Once Kate's kite reaches a height of 50 ft (above her hands), it rises no higher but drifts due east in a wind blowing 7 ft divided by s. How fast is the string running through Kate's hands at the moment that she has released 107 ft of string?

dz  = 7.136 (answer)

Explanation:

given height  for kate's kite   = 50 ft  (say y)

due to drift it move towards east =  dx = 7 ft  

string maximum length          = 107 ft ( say z)

we have to find change in z  

that is  dz

it will form a right angle triangle for x , y and z  where x is base y is height and z is hypotenuse

so we get according to Pythagoras Theorem

...............(i)

by derivative both side  consider y as constant

from (i)  equation

now put the value and find dz

after solving these  we get

dz  = 7.136 (answer)