Applications Of Derivatives Question 186
Question: A ladder 10 m long rests against a vertical wall with the lower end on the horizontal ground. The lower end of the ladder is pulled along the ground away from the wall at the rate of 3 cm/sec. The height of the upper end while it is descending at the rate of 4 cm/sec is
[Kerala(Engg.) 2005]
Options:
A) $ 4\sqrt{3} $ m
B) $ 5\sqrt{3} $ m
C) $ 5\sqrt{2},m $
D) 8 m
E) 6 m
Show Answer
Answer:
Correct Answer: B
Solution:
We have $ x^{2}+y^{2}=10^{2} $
therefore $ 2x\frac{dx}{dt}+2y\frac{dy}{dt}=0 $
therefore $ x.3+y.(-4)=0 $
$ x=\frac{4}{3}y $ . Thus, $ {{( \frac{4}{3}y )}^{2}}+y^{2}=10^{2}\Rightarrow y=6 $ m.
BETA
