Question

A kite is moving horizontally at height of 151.5 meters. If the speed of kite is 10m/s how fast is the string being let out when the kite is 250m away from the boy who is flying the kite? The height of boy is 1.5m.

Answer 1

Given height at which the kite is flying is

AC=151.5mAC=151.5m

Height of the boy = BC=1.5mBC=1.5m

⇒AB=h=151.5−1.5=150⇒AB=h=151.5−1.5=150

By applying pythagoras theorem in ΔABEΔABE,

AB2+BE2=AE2AB2+BE2=AE2

i.e.,h2+x2=y2(1)i.e.,h2+x2=y2(1)

when x=BE=250mx=BE=250m,

1502+2502=AE21502+2502=AE2

⇒AE=y=291.5m⇒AE=y=291.5m

Differentiating equation (1) w.r.t. tt we get

2x.dxdt2x.dxdt=2y.dydt=2y.dydt

⇒xdxdt=ydydt⇒xdxdt=ydydt

( Since height is always a constant )

Step 2

Given dxdtdxdt=10m/sec=10m/sec and x=250mx=250m

Now substituting the values for x,yx,y and dxdtdxdt we get

10×250=291.5×dydt10×250=291.5×dydt

⇒dydt=10×250291.5⇒dydt=10×250291.5

=8m/sec=8m/sec

Hence the rate at which the string is released is 8m/sec