Question

A girl of height 90 cm is walking away from the base of a lamb-post at a speed of 1.2 m/sec if the lamp is 3.6 m above the ground find the length of her shadow after 4 seconds

• A. $1.6m$
• B. $1.4m$
• C. $4.2m$
• D. $3.6m$

Answer 1

The correct option is A $1.6m$

R.E.F image

Lamp post $\left(AB\right):3.6m$

Girl's height $:90cm=0.9m\left(CD\right)$

Speed $=1.2m/s$

Let the shadow length be $\Delta E$

we know that speed $=\frac{dist.}{time}$

$1.2=\frac{BD}{4}\Rightarrow BD=4.8m$

In $\Delta ABE$ and $\Delta CDE$

$\angle E=\angle E$ (common)

$\angle B=\angle D$ (Both ${90}^{\circ }$)

$\therefore \Delta ABE\sim \Delta CDE$

$\because \frac{BE}{DE}=\frac{AB}{CD}$

$\Rightarrow \frac{BD+DE}{DE}=\frac{AB}{CD}\Rightarrow \frac{4.8+DE}{DE}=\frac{3.6}{0.9}$

$\Rightarrow DE=1.6m$