A kite is moving horizontally at a height of `151.5 m`. If the speed of the 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 the boy is 1.5 m. (A) `8` m/s (B) `12 ` m/s (C) `16` m/s (D) `19` m/s

Explanation

We have, height `(h)=151.5 m`, speed of kite `(v)=10 {m} / {s}`


Let `C D` be the height of kite and `A B` be the height of body.


`therefore quad frac(d x)(d t) =10`


From the figure, we have


In angled `triangle C E A`,


` Rightarrow quad A E^{2}+E C^{2} =A C^{2} x^{2}+(150)^{2} =y^{2} `


Differentiating w.r.t. `x`, we get



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