question_answer

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]

A)            \[4\sqrt{3}\]m

B)            \[5\sqrt{3}\]m

C)            \[5\sqrt{2}\,m\]

D)            8 m

E)                 6 m

Correct Answer: B

Solution :

  We have \[{{x}^{2}}+{{y}^{2}}={{10}^{2}}\]            Þ \[2x\frac{dx}{dt}+2y\frac{dy}{dt}=0\] Þ  \[x.3+y.(-4)=0\]            \[x=\frac{4}{3}y\]. Thus, \[{{\left( \frac{4}{3}y \right)}^{2}}+{{y}^{2}}={{10}^{2}}\Rightarrow y=6\]m.