Question

A man is flying a kite, he holds a string 1.5m above the level ground and the string is released at the rate of 2 m/s. As the kite moves horizontally at an altitude of 51.1m, assuming that the string is straight, find the rate at which the kite is moving horizontally when there are 80m of cord is out.

Answer 1

Make a sketch showing a right-angled triangle.
The height of the triangle is to be constant at 49.6 m
( (51.1 - 1.5) , I have a feeling that was supposed to be 51.5 m)

At a given time of t seconds, let the horizontal length of the triangle be x
and let the length of the string be r
given : dr/dt = 2 m/s
find : dx/dt when r = 80

r^2 = x^2 + 49.6^2
when r = 80
x^2 = 80^2 - 49.6^2 = ....
x = 62.768..

2r dr/dt = 2x dx/dt + 0
dx/dt = r dr/dt/x
= ....