Question

A man of height 1.8m is moving away from a lamp post at the rate of 1.2m/s.if the height of the lamp post is 4.5m. Then the rate at which the shadow of the man is lengthening is?

Answer 1

1st second

height of man = 1.8 m
height of the lamp = 4.5
$\frac{4.5}{1.8}$ = $\frac{5}{2}$

2nd second 

height of man = 1.8 m
height of the lamp = 4.5
$\frac{4.5}{1.8}$ = $\frac{4.2+x}{x}$
x = 2.8

3rd second

height of man = 1.8 m
height of the lamp = 4.5
$\frac{4.5}{1.8}$ = $\frac{5.4+x}{x}$
x = 3.6

1st second, length of the shadow of man = 2 m

2nd second, length of the shadow of man = 2.8 m

3rd second, length of the shadow of man = 3.6 m

The length of the shadow of man = 0.8 m/s

Answer 2

For first second,
4.5/1.8 = 1.2 + x/x
4.5x = 21.6 + 1.8x
21.6 = 2.7x
x = 21.6/2.7
x = 8

For second second,
4.5/1.8 = 2.4 + x/x
x = 2.8

Rate = 2.8-8 = 0.8 m/s