Question

A kite is 120 m high and 130 m of string is out. If the kite is moving away horizontally at the rate of 52 m/sec, find the rate at which the string is being paid out.

Answer 1

Let P be the position of the kite and PR be the position of the string. Let QR = x and PR = y. Then from figure by applying Pythagoras theorem, we get

Differentiating the above equation with respect to time, we get

Now the kite is moving away horizontally at the rate of 52m/sec, so \(\frac{dx}{dt}\) = 52 m/sec, so the above equation becomes

So when the string is 130m, y = 130m equation (i) become,

Substituting the value of x and y in equation (ii), we get

Hence the rate at which the string is being paid out is 20m/sec