A man of height 2m walks directly away from a lamp of height 5m, on a level road

Discussion Forum : Application Of Derivatives

Question -

A man of height 2m walks directly away from a lamp of height 5m, on a level road at 3 m/s. The rate at which the length of his shadow is increasing is

Options:

A . 1m/s

B . 2m/s

C . 3m/s

D . 4m/s

Answer: Option B
:
B

Let be the lamp and PQ be the man and OQ=x metre be his shadow and let MQ =y metre.

$∴ \frac{d y}{d t}$ =speed of the man
=3 m/s (given)
$∵ Δ O P Q$ and $Δ O L M$ are similar
$∴ \frac{O M}{O Q} = \frac{L M}{P Q} \Rightarrow \frac{x + y}{x} = \frac{5}{2} \Rightarrow y = \frac{3}{2} x ∴ \frac{d y}{d t} = \frac{3}{2} \frac{d x}{d t} \Rightarrow 3 = \frac{3}{2} \frac{d x}{d t} \Rightarrow \frac{d x}{d t} = 2 m / s$

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