question_answer

A man of height \[1.8\] metre is moving away from a lamp post at the rate of \[1.2\text{ }m/sec\]. If the height of the lamp post be \[4.5\] metre, then the rate at which the shadow of the man is lengthening is

A) \[0.4\text{ }m/sec\]            

B) \[0.8\text{ }m/sec\]

C) \[1.2\text{ }m/sec\]          

D)   None of these

Correct Answer: B

Solution :

                   

\[\frac{dy}{dt}=1.2\]. According to the figure \[\frac{4.5}{1.8}=\frac{x+y}{x}\]    \[\frac{5}{2}=\frac{x+y}{x}\Rightarrow 3x=2y\]

\[x=\frac{2}{3}y\Rightarrow \frac{dx}{dt}=\frac{2}{3}\frac{dy}{dt}\]

\[\therefore \] required rate of length of shadow \[\frac{dx}{dt}=0.8m/s.\]