JEE Main & Advanced
Mathematics
Applications of Derivatives
Question Bank
Critical Thinking
question_answer
A man of height 1.8 metre 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 metre, then the rate at which the shadow of the man is lengthening is [MP PET 1989]
A)\[0.4\,\,m/\sec \]
B)\[0.8\,\,m/\sec \]
C)\[1.2\,\,m/\sec \]
D)None of these
Correct Answer:
B
Solution :
\[\frac{dy}{dt}=1.2.\]According to the figure \[x=\frac{2}{3}y\] Þ \[\frac{dx}{dt}=\frac{2}{3}.\frac{dy}{dt}\]
\[\therefore \] Required rate of length of shadow \[\frac{dx}{dt}=0.8m/s\].