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 grough away from the wall at the rate of $3cm/s$. The height of the upper end while is 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)

$6m$

Let $AB=xm,BC=ym$ and $AC=10m$

$x^2+y^2=100$ ...(i)

On differentiating w.r.t. $x,$ 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 Eq. (i) we get

$\frac{16}{9}{y}^2+y^2=100$

$\Rightarrow y^2=\frac{100\times 9}{25}=36\Rightarrow y=6m$