Question

A girl with height 90 cm walks away from the base of lamp-post at a speed of 1.2 m/sec. lithe lamp is 3.6 m above the ground. Find the length of her shadow after 4 seconds.

Answer 1

Let AB = Lamp post

CD = girl

DE = shadow of the girl,

BD = 1.2 × 4 = 4.8 m

Let shadow of girl,

DE = ‘a’ m

In ∆ABE and ∆CDE

∠B = ∆(each 90°)

∠E = ∠E (comman angle)

∆ABE ~ ∆CDE by (AA criterion)

therefore, BE/DE = AB/CD ⇒ (4.8 + a)/a = 3.6/0.9

⇒ 4.8 + a = 4a

⇒ 3 a = 4.8

⇒ a = 1.6 m

Thus after 4 sec. length of girl’s shadow will be 1.6 m