Applications Of Derivatives Question 407
Question: 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
Options:
A) 5 m/h
B) $ \frac{5}{2} $ m/h
C) $ \frac{5}{3} $ m/h
D) $ \frac{5}{4} $ m/h
Show Answer
Answer:
Correct Answer: B
Solution:
$ \frac{dy}{dt}=5,\ \ \ \frac{dx}{dt}=- $ $ \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 $ .
BETA
