Question

A man $2$ metres tall walks away from a lamp post $5$ metres height at the rate of $4.8$ km/hr. The rate of increase of the length of his shadow is

• A. $1.6$ km/hr
• B. $6.3$ km/hr
• C. $5$ km/hr
• D. $3.2$ km/hr

Answer 1

The correct option is D $3.2$ km/hr

Given $\frac{dx}{dt}=4.8km/hr$

We have $\frac{5}{x+y}=\frac{2}{y}$

$\Rightarrow 3y=2x$

$\Rightarrow 3\frac{dy}{dt}=2\frac{dx}{dt}$

$\Rightarrow \frac{dy}{dt}=3.2km/hr$