question_answer

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, then find the length of her shadow after 4 s.

A) 8 m                              

B) 1.6 m

C) 2.8 m               

D) 2 m

Correct Answer: B

Solution :

Let length of shadow = DE = x m

BD = Distance covered by the girl in 4 s

\[=1.2\times 4=4.8\text{ }m\]

Also, in \[\Delta ABE\] and \[\Delta CDE\]

and \[\angle B=\angle D\]

\[\Rightarrow \]   \[\angle A=\angle C\]and \[\angle E=\angle E\]

\[\therefore \] \[\Delta ABE=\Delta CDE\]

\[\therefore \]\[\frac{BE}{DE}=\frac{AB}{CD}\]\[\Rightarrow \]\[\frac{4.8+x}{x}=\frac{3.6}{0.9}\]

\[\Rightarrow \]   \[4.8+x=4x\]\[\Rightarrow \]\[x=1.6\,m\]