question_answer

A man 2metre high walks at a uniform speed 5 metre/hour away from a lamp post 6 metre high. The rate at which the length of his shadow increases is

A)  5 m/h

B)            \[\frac{5}{2}\]m/h

C)  \[\frac{5}{3}\]m/h

D)   \[\frac{5}{4}\]m/h

Correct Answer: B

Solution :

           \[\frac{dy}{dt}=5,\ \ \ \frac{dx}{dt}=?\]                    From figure, \[\frac{x}{2}=\frac{x+y}{6}\Rightarrow 4x=2y\Rightarrow x=\frac{1}{2}y\]                    Hence \[\frac{dx}{dt}=\frac{1}{2}\frac{dy}{dt}=\frac{5}{2}metre/hour\].