Question

A girl of height 100 cm is walking away from the base of the lamp post at a speed of 1.5 metre per second if the lamp is 4 metre above the ground find the length of her shadow after 5 seconds.

Answer 1

Answer:

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)

∴ Length of her shadow after 4 second is 160 cm