As shown in the given figure, a girl of height 90 cm is walking away from the base of a lamp post at a speed of 1.2 m/s. If the lamp is 3.6 m above the ground, find the length of her shadow after 4 seconds.
Show Hint
Always ensure all units are consistent (convert cm to m) before substituting values into similarity ratios.
Given:
Height of lamp post = 3.6 m
Height of girl = 90 cm = 0.9 m
Speed of girl = 1.2 m/s
Time = 4 seconds
Distance walked by the girl from the lamp post:
\[
BD = 1.2 \times 4 = 4.8\ \text{m}
\]
Let the length of her shadow = DE meters.
Using similar triangles:
Triangle ABE (lamp and its shadow) is similar to triangle CDE (girl and her shadow).
So,
\[
\frac{\text{height of lamp}}{\text{height of girl}}
=
\frac{\text{distance from lamp to tip of shadow}}{\text{distance from girl to tip of shadow}}
\]
Substitute values:
\[
\frac{3.6}{0.9} = \frac{BD + DE}{DE}
\]
Simplify left side:
\[
\frac{3.6}{0.9} = 4
\]
So,
\[
4 = \frac{4.8 + DE}{DE}
\]
Cross multiply:
\[
4DE = 4.8 + DE
\]
\[
4DE - DE = 4.8
\]
\[
3DE = 4.8
\]
\[
DE = \frac{4.8}{3} = 1.6\ \text{m}
\] Final Answer:
The length of the girl's shadow after 4 seconds is:
\[
\boxed{1.6\ \text{m}}
\]
