Question

A $16$ m long cord is attached to the point C and passes over two pulleys A and D. Pulley A is attached to the smooth collar that travels along vertical rod. When DB = $6$ m, end B of the cord is pulled down with velocity of $8\text{m/s}$. Speed of the collar at this instant in $\text{m/s}$ is (Write until two digits after the decimal point)

Answer 1

Total length of the string is,
$2\left(\sqrt{y^2+3^2}\right)+y^{\prime }=L$
$\frac{\text{/}2}{\text{/}2}\frac{2y\frac{dy}{dt}}{\sqrt{y^2+9}}+\frac{d{y}^{\prime }}{dt}=0$
$\frac{dy}{dt}=-\frac{d{y}^{\prime }}{dt}\frac{\sqrt{y^2+9}}{2y}=\frac{-8\times 5}{2\times 4}=-5$
So the speed is $5\text{m/s}$