Question

A ladder $10m$ 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 $3cm/s$. The height of the upper end while it is descending at the rate of $4cm/s$, is

• A. $4\sqrt{3}m$
• B. $5\sqrt{3}m$
• C. $6m$
• D. $8m$

Answer 1

Answer: (C)

Let $AB=xm$,
$BC=ym$ and $AC=10m$
$\therefore x^2+y^2=100...\left(i\right)$
On differentiating $\left(i\right)$ w.r.t. $t$, we get

$2x\frac{dx}{dt}+2y\frac{dy}{dt}=0$
$\Rightarrow 2x\left(3\right)-2y\left(4\right)=0$
$\Rightarrow x=\frac{4y}{3}$
On putting this value in $\left(i\right)$, we get
$\frac{16}{9}{y}^2+y^2=100$
$\Rightarrow y^2=\frac{100\times 9}{25}=36$
$\Rightarrow y=6m$