Question

The rate of increase of length of the shadow of a man 2 metres height, due to a lamp at 10 metres height, when he is moving away from it at the rate of 2m/sec, is

• A. $\frac{1}{2}$m/sec
• B. $\frac{2}{5}$m/sec
• C. $\frac{1}{3}$m/sec
• D. $5m/sec$

Answer 1

Answer: (A)

$\frac{1}{2}$m/sec

Let $x$ be the length between man and lamp, and $y$ be the length of shadow.

Given ,$\frac{dx}{dt}=2m/sec$

From the figure,

$\frac{10}{x+y}=\frac{2}{y}$

$\Rightarrow 8y=2x$

$8\frac{dy}{dt}=2\frac{dx}{dt}$

$\Rightarrow \frac{dy}{dt}=\frac{1}{4}\left(2\right)=\frac{1}{2}$ m / sec