Question

A girl of height $90\text{cm}$ is walking away from the base of a lamp-post at a speed at $1.2\text{m/sec}$. If the lamp is $3.6\text{m}$ above the ground, find the length of her shadow after $4$ seconds.

Answer 1

Given,

• Girl is walking away from the base of the lamp-post and let the girl be at point D after $4$ seconds
• speed $=1.2\text{m/sec}$
• time $=4\text{sec}$

$\text{speed}=\frac{\text{distance}}{\text{time}}$

$⟹1.2=\frac{\text{distance}}{4}$

$⟹\text{distance}=AD=12\times 4=4.8\text{m}$

Consider $△ABC$ and $△DBE$

$\angle CAB=\angle EDB={90}^{\circ }$

$\angle CBA=\angle EDB$ (common angle)

So by $AA$ similarity, $△ABC\sim △DBE$

Hence, $\frac{AC}{DE}=\frac{AB}{DB}$

$⟹\frac{AC}{DE}=\frac{AD+DB}{DB}$

$⟹\frac{3.6}{0.9}=\frac{4.8+DB}{DB}$

$⟹4DB=4.8+DB$

$⟹3DB=4.8$

$⟹DB=1.6$

Hence the length of the shadow $1.6\text{m}$