Question

A boy of height 120 cm is walking away from the base of a lamp
post at a speed of 1.8 m/sec. If the lamp is 4.2 m above the
ground, find the length of the shadow after 4 seconds

Answer 1

The length of the shadow = 2.88 m

Step-by-step explanation:

Given :

• Height of the boy = 120 cm
• Height of the lamp = 4.2 m
• Speed = 1.8 m/s
• Time = 4 seconds

According to the question :

Let's first convert Height of the boy in meters.

So, $\sf{120\:cm\:=\:1.2\:meter}$

We know that, Speed = 1.8 m/s, And Hence Distance after 4 second would be,

$\sf{a\:= 1.8\:\times\:4\:=\:7.2\:m}$

(Refer the attachment for the figure)

Solving :

As they are similar triangles,

$\sf\implies{\dfrac{1.2}{4.2}}\:=\:{\dfrac{b}{a\:+\:b}}$

Substituting 'a' value :

$\sf\implies{\dfrac{1.2}{4.2}}\:=\:{\dfrac{b}{7.2\:+\:b}}$

$\sf\implies{1.2\:(7.2\:+\:b)\:=\:4.2b}$

$\sf\implies{1.2\:(7.2\:+\:b)\:=\:4.2b}$

$\sf\implies{8.64\:+\:1.2b)\:=\:4.2b}$

$\sf\implies{8.64\:=\:4.2b\:-\:1.2b}$

$\sf\implies{8.64\:=\:3b}$

$\sf\implies{b\:=\:{\dfrac{8.64}{3}}}$

$\sf\implies{b\:=\:{{\cancel{\dfrac{8.64}{3}}}}}$

$\sf\implies{b\:=\:2.88}$

Hence, the length of the shadow = 2.88 m.