Question

A girl of height 100 cm is walking away from the base of a lamp post at a speed of 1.9m/s .if the lamp is 5m above the ground, find the length of her shadow after 4 seconds.

Answer 1

The length of girl's shadow after 4 seconds is 1.9 meters

Step-by-step explanation:

Given as :

The height of lamp post = H = 5 m

The height of girl = h = 100 cm = 1 m

The speed of girl walking away = 1.9  m/sec

Let The length of girl's shadow after 4 sec = x m

According to question

From figure

The height of lamp post  = AB = 5 m

The height of girl = CD = 1 m

The girl will walk BD distance in 4 sec

∵  Distance = Speed × time

So, BD = 1.9 m/sec × 4 sec

i.e BD = 7.6 m

Again

From figure, In Δ AEB   and Δ CED

∠B = ∠ D = 90°

∠ E = ∠E         (common angle )

So,  Δ AEB  ≈ Δ CED

$\dfrac{AB}{CD}$  = $\dfrac{BE}{DE}$

Or,  $\dfrac{5 m}{1 m}$ = $\dfrac{BD + DE}{DE}$

Or,  5 = $\dfrac{BD}{DE}$ + 1

Or, $\dfrac{BD}{DE}$  = 5 - 1

Or, $\dfrac{7.6 m}{DE}$  = 4

∴   DE = $\dfrac{7.6 m}{4}$

i.e  DE = 1.9 meters

So, The length of shadow = DE = 1.9 meters

Hence, The length of girl's shadow after 4 seconds is 1.9 meters Answer