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 the value of length of her shadow after 4s is

A) 3.2m

B) 4.8m

C) 1.6m

D) 3.6m

Correct Answer: C

Solution :

Let AB be the lamp-post, CD be the girl and D be the position of girl after 4s.

Again, let DE = x m be the length of shadow of the girl.

Given, CD = 90 cm = 03 m, AS = 3.6 m and speed of the girl =1.2 m/s

\[\therefore\]Distance of the girl from lamp-post after 4s,

\[BD=1.2\,\times 4=4.8\,\,m\]

[\[\because\]distance = speed \[\times\] time]

In \[\Delta ABE\] and      \[\Delta CDE\],

\[\angle B=\angle D\]      [each \[90{}^\circ\]]

\[\angle E=\angle E\]       [common angle]

\[\therefore \Delta ABE\tilde{\ }\Delta CDE\]

[by AA similarity criterion]

\[\Rightarrow \frac{BE}{DE}=\frac{AB}{CD}\]                 … (i)

[since, corresponding sides of similar triangles are proportional]

On substituting all the values in Eq. (i), we get

\[\frac{4.8+x}{x}=\frac{3.6}{0.9}\]

\[\left[ \because \,\,\,BE=BD+DE=4.8+x \right]\]

\[\Rightarrow \,\,\,\frac{4.8+x}{x}=4\]

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

\[\Rightarrow \,\,\,\,3x=4.8\]

\[\Rightarrow \,\,\,\,=\frac{4.8}{3}=1.6\,\,\,m\]

Hence, the length of her shadow after 4s is 1.6 m.