Question: A boy of height 1.3 m is walking away from the base of a lamp post at a speed of 0.9 m/sec. Find the height of the lamp post from the ground, if the shadow of the boy is 2.4 m after walking for 5 sec.
Solution:Given that,
Height of the boy = 1.3m
Speed of the boy = 0.9 m/s
∴ Distance travelled by boy in 5 sec = 0.9 × 5 = 4.5m
∴ Total distance of shadow of boy and distance from base of lamp post = 2.4 + 4.5 = 6.9 m
Let the height of lamp post be 'h' m
According to question,
⇒ 1.3/2.4 = h/6.9
⇒ h = (6.9 × 1.3)/2.4
⇒ h = 3.7375 = 3.74m
So, The height of the lamp post is 3.74 meters.