Question

A boy of height 60 cm is walking away from the base of a building at a speed of 2.2 m/s. If the height of the building is 7.2 m, then find the length of his shadow after 5 seconds.

• A. $2m$
• B. $3m$
• C. $1m$
• D. $4m$

Answer 1

The correct option is C $1m$


Let AB be the building and EC be the boy.
Given: Height of building, AB = 7.2 m
Boy's height = 60 cm = 0.6 m
Boy's speed = 2.2 m/s

$\text{Let}x\text{be the length of his shadow}\text{and y be the distance between}\text{building and the boy after 5 seconds.}$

Distance travelled by the boy in 5 seconds
= Speed $\times$ Time
= $2.2\times 5=11m$

$\Rightarrow y=11m$

$\text{In}\Delta ABD\text{and}\Delta ECD$,

$\angle ABD=\angle ECD={90}^{\circ }$

$\angle ADB=\angle EDC\text{(Common in both the triangles)}$

$\therefore \Delta ABD\sim \Delta ECD\text{(By AA similarity criterion)}$

$\Rightarrow \frac{AB}{EC}=\frac{BD}{CD}\text{(Corresponding sides of similar}\text{triangles are in the same ratio)}$

$\Rightarrow \frac{7.2}{0.6}=\frac{y+x}{x}$

$\Rightarrow 12=\frac{11+x}{x}$

$\Rightarrow 12x=11+x$

$\Rightarrow x=1m$

$\text{So, the length of his shadow after}\text{5 seconds is 1 m.}$