A ladder of length 17 metres rests with one end against a vertical wall. The lower end of the ladder is pulled away from the wall at the rate of 1.5 metres/minute. The rate at which the upper end of the ladder falls when its bottom end is 8 metres away from the wall is :

$-\frac{4}{5}$ metres /minute

The correct answer is Option (2) → $-\frac{4}{5}$ metres /minute

The length of ladder is constant and equal to 17 m.

$x^2+y^2=17^2=289$ [By Pythagoras]

$\frac{dx}{dt}=1.5m/min$

$2x\frac{dx}{dt}+2y\frac{dy}{dt}=0$

$⇒\frac{dy}{dt}=\left(x×\frac{dx}{dt}\right)×\frac{1}{y}$

$=\frac{-8×1.5}{15}=-\frac{4}{5}$ metres /minute