In a computer simulation, a drone is programmed to always fly directly towards a moving target. The target moves north from a specific point at a constant speed of $1$ unit per time step. The drone starts its pursuit $3$ units east of the starting point of the target, moving at a speed of $s>1$ unit per time step. The path followed by the drone is given by the equation $y=\frac{s}{2}[\frac{x^{\frac{s+1}{s}}}{s+1}-\frac{x^{\frac{s-1}{s}}}{s-1}]+\frac{s}{s^2-1}$. For a simulation where $s=3$, what is the $y$-coordinate of the drone's position when $x=8$ units? Also, plot the graph for $s=3$.