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A kite is 120 ~m high and 130 ~m of string is out. If the kite is moving away horizontally at the rate of 39 ~m / sec , then the rate at which the string is being out, is

Options

  1. A12 ~m / sec .
  2. B15 ~m / sec .
  3. C18 ~m / sec .
  4. D20 ~m / sec .

Correct answer

B. 15 ~m / sec .

Step-by-step solution

Let 'P' be the position of the kite and PR be the string. Let QR =x and PR =y By Pythagoras theorem, aligned & - PR ^2= PQ ^2+ QR ^2 & y^2=(120)^2+x^2... (i) aligned Differentiating w.r.t.t, we get aligned & 2 y d y dt =2 x d x dt & y d y dt =x d x dt ... (ii) aligned Now, kite is moving away horizontally at the rate of 39 ~m / sec . aligned & d x dt =39 ~m / sec & From (i), & (130)^2=(120)^2+x^2 & x^2=16900-14400 & x^2=2500 & x=50 & From (ii), & 130 d y dt =50 39 & d y dt = 50 39 130 =15 ~m / sec aligned

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