Question

A man of height 1.8 metre is moving away from a lamp post at the rate of 1.2 m/sec . If the height of the lamp post be 4.5 metre , then the rate at which the shadow of the man is lengthening is

• A. $0.4m/sec$
• B. $0.8m/sec$
• C. $1.2m/sec$
• D. None of these

Answer 1

The correct option is B $0.8m/sec$

$1^{st}$ second

height of man $=1.8m$

height of the lamp$=4.5m$

$\frac{4.5}{1.8}=\frac{5}{2}$

$2^{nd}$ second

height of man $=1.8m$

height of the lamp$=4.5m$

$\frac{4.5}{1.8}=\frac{4.2+x}{x}$

$\Rightarrow 4.5x=7.56+1.8x$

$\Rightarrow 4.5x-1.8x=7.56$

$\Rightarrow 2.7x=7.56$

$\Rightarrow x=\frac{7.56}{2.7}=2.8$

$3^{rd}$ second

height of man$=1.8m$

height of the lamp$=4.5m$

$\frac{4.5}{1.8}=\frac{5.4+x}{x}$

$\Rightarrow 4.5x=9.72‬+1.8x$

$\Rightarrow 4.5x-1.8x=9.72$

$\Rightarrow 2.7x=9.72$

$\Rightarrow x=\frac{9.72}{2.7}=3.6$

$1^{st}$ second, length of the shadow of man $=2m$

$2^{nd}$ second, length of the shadow of man $=2.8m$

$3^{rd}$ second, length of the shadow of man $=3.6m$

The length of the shadow of man $=2.8-2=3.6-2.8=0.8m{s}^{-1}$

$\therefore$length of the shadow of man is $0.8m{s}^{-1}$