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

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

Answer 1

Answer: (C)

$6\,m$

Answer 2

Let $AB = x\, m$, $BC = y\, m$ and $AC = 10\, m$ $\therefore x^{2 }+ y^{2}= 100 \quad...\left(i\right)$ 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 $\frac{16}{9} y^{2} + y^{2} = 100$ $\Rightarrow y^{2} = \frac{100 \times 9}{25} = 36$ $\Rightarrow y = 6\,m$