Question

A man of height 1.8 m is moving away from a lamp post at the rate of 1.2 m/sec. If the height of the lamp post be 4.5 meter, then the rate at which the shadow of the man is lengthening

• A. 0.4 m/sec
• B. 0.8 m/sec.
• C. 1.2 m/sec.
• D. None

Answer 1

Answer: (B)

0.8 m/sec.

Answer 2

$\frac{dy}{dt} = 1.2$ According to the figure,

$x = \frac{2}{3}y$

⇒ $\frac{dx}{dt} = \frac{2}{3}.\frac{dy}{dt}$

⇒ Rate of length of shadow $\frac{dx}{dt} = 0.8m/s$.