Question

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 is 3.6 m above the ground, find the length of her shadow after 4 seconds.

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.

Answer 1

We have,

Height of girl = 90 cm = 0.9 m

Height of lamp-post = 3.6 m

Speed of girl = 1.2 m/sec

∴ Distance moved by girl (CQ) = Speed × Time

= 1.2 × 4

= 4.8 m

Let length of shadow (AC) = x cm

In ΔABC and ΔAPQ

∠ACB = ∠AQP   ...[Each 90°]

∠BAC = ∠PAQ   ...[Common]

Then, ΔABC ~ ΔAPQ   ...[By AA similarity]

∴ `(AC)/(AQ) = (BC)/(PQ)`   ...[Corresponding parts of similar Δ are proportional]

⇒ `x/(x + 4.8) = 0.9/3.6`

⇒ `x/(x + 4.8) = 1/4`

⇒ 4x = x + 4.8

⇒ 4x – x = 4.8

⇒ 3x = 4.8

⇒ `x = 4.8/3`

⇒ x = 1.6 m

∴ Length of shadow = 1.6 m