Question

A man of height $2$ m walks at a uniform speed of $5$ km/hour away from a lamp post of 6m height. His shadow length increases at the rate of

• A. $12.5$ km/hour
• B. $2.5$ km/hour
• C. $3$ km/hour
• D. $3.5$ km/hour

Answer 1

The correct option is B $2.5$ km/hour


$△ABD$ is similar to $△ECD$ so,
$\frac{6}{2}=\frac{x+y}{y}\Rightarrow \frac{x}{y}=2\Rightarrow \frac{x}{2}=y$
We know that $\frac{dx}{dt}=5$ km/hour,
$\frac{dy}{dt}=\frac{1}{2}\times \frac{dx}{dt}=2.5$ km/ hour