(Q23) A girl of height 90 cm is walking away from the base of a lamp-post at a speed of 1.2 m/sec. If the lamp-post is 3.6 m above the ground, find the length of her shadow after 4 seconds.

Solution :

ABCEDx90 cm4.8 m480 cm3.6 m = 360 cm

Given : A lamp-post AB of height = 3.6m = 360cm

Speed of the girl = 1.2 m/sec.

Distance travelled in 4 sec = Speed x Time = 1.2 × 4 = 4.8 m = 480 cm.

CD, height of the girl = 90 cm.

Let the length of the shadow at a distance of 4.8 m from the lamp post = x cm.

From the figure,

∆ABE ~ ∆DCE

[∵ ∠B = ∠C = 90o, ∠E = ∠C common ,(A.A. similarity)]

Hence,
AB
DC
 =
BE
CE
 =
AE
DE
∴
90
 =
480 + x
x
⇒ =
480 + x
x

⇒ x = + x

⇒ x - x =

⇒ x =

⇒ x = cm = m

⇒ Length of the shadow = m