Question

A boy of height 150 cm is walking away from the base of a lamp-post at a speed of 1.5 m/s. If the lamp is 4.5 m above the ground, find the length of his shadow after 6 seconds.

• A. 1.5 m
• B. 4.5 m
• C. 9 m
• D. 6 m

Answer 1

The correct option is B

4.5 m

In the figure,
AB is the height of the lamp-post
DE is the height of the boy and EC is the length of the shadow.
BE is the distance covered by the boy in 6 seconds = 1.5 6 = 9
$\angle ABC$ and $\angle DEC$ are 90. (Since lamp-post and the boy are perpendicular to the ground.)
$\angle ACB$ is common for $\Delta ABC$ and $\Delta DEC$.
$\Delta ABC$ and $\Delta DEC$ are similar triangles.
By similar triangle property,
$\frac{AB}{DE}=\frac{BC}{EC}\frac{4.5}{1.5}=\frac{BE+EC}{EC}3=\frac{9+EC}{EC}$
Solving the equation gives,
$3\times EC=9+ECEC=\frac{9}{2}=4.5m$