1. A girl of height 90cm is walking away from the base of a lamp-post at a speed of 1.2m/s. If the lamp is 3.6m above the ground. Find the length of her shadow after 45.

Length of her shadow after 4 second is 160 cm

Explanation:

Let the girl be at point D on the ground from the lamppost after 4 sec.

BD = 1.2 m/sec × 4 sec = 4.8 m = 480 cm

Suppose the length of the shadow of the girl be x cm when she at position D.

ED = x cm

In ∆EDC and ∆EBA

∠EDC = ∠EBA  (90°)

∠DEC = ∠BEA (Common)

∆EDC ∼ ∆EBA  (AA similarity)

EC/EA = DC/BA = ED/BE

EC/EA = ED/BE

90cm/360cm = x cm/(480+x) cm

1/4 = x/x+480

4x = x + 480

3x = 480

x = 480/3

x = 160

(corresponding sides or proportional)

So, the length of her shadow after 4 second is 160 cm.