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Question

An aeroplane is flying horizontally at a height of $\frac{2}{3}$ km with a velocity of 15 km/hr. The rate at which it is receding from a fixed
point on the ground which is passed over 2 minutes ago.

Moderate

Solution

$\begin{matrix} l^{2} = x^{2} + h^{2} \\ 2 l \frac{d l}{d t} = 0 + 2 x \frac{d x}{d t} \\ \frac{d l}{d t} = \frac{x}{l} \frac{d x}{d t} = \frac{6}{5} \times 15 = 9 km / hr \\ x = \frac{1}{2} h = \frac{2}{3} \\ l^{2} = \frac{1}{4} + \frac{4}{9} = \frac{25}{56} \\ l = 5 / 6 \end{matrix}$

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