Answer
$v=2.19m/s$
Work Step by Step
The velocity of the cylinder can be calculated as
$F_s-mg=0$
$\implies 120x_{\circ}-4\times 9.81=0$
$\implies x_{\circ}=0.327m$
We know that
$\Sigma F_y=ma_y$
$F_s-mg-60=ma_y$
$\implies 120(0.327+s)-4\times 9.81-60=-4a$
$\implies a=15-30s$
As $a=\frac{dv}{dt}=v\frac{dv}{ds}$
$\implies ads=vdv$
$\implies \int_0 ^s (15-30)ds=\int_0^v vdv$
$\implies 15s-15s^2=\frac{v^2}{2}$
$\implies 15\times 0.2-15(0.2)^2=\frac{v^2}{2}$
This simplifies to:
$v=2.19m/s$
