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 :
Answer & explanation
Correct answer: option 2
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