Question

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

Answer 1

Given: a boy of n height 1.5 m is flying a kite at a height of 151.5 m. The kite is moving with a speed of 10m/s. And the kite is 250 m away from the boy.

To find the speed at which the string is let out

Explanation: the below figure shows the above situation,

From the above figure,

Height of the kite, H = AD = 151.5 m

Height of the boy, b = BC = 1.5 m

Distance between kite and boy, x = CD = BE = 250 m

And BA is the length of the string = y

So, we need to find out the rate of increase of the string

From figure, h = AE

= AD-ED

= 151.5-1.5

= 150m

From figure it is clear that ΔABE forms right-angled triangle

Now applying the Pythagoras theorem, we get

AB² = BE²+AE²

Or y² = x²+h²………..(i)

Now substituting the corresponding values, we get

y² = (250)²+(150)²

⇒ y² = 62500+22500

⇒ y² = 85000

⇒ y = 291.5m………..(ii)

Now differentiate equation (i) with respect to time, we get

Now given the kite is moving with a speed of 10m/s, so

Now substituting corresponding value in equation (iii), we get

Hence the string is let out at a rate of 8.6m/s.