$L$. The pendulum’s angular velocity at the moment the pendulum stops at the stop-bar and the projectile is ejected from its holder is $$\dot \theta = 
   \sqrt{2 \frac{M_{pend} }{I_{pend}} R_{cm} g 
     (\cos \theta_{sb} - \cos \alpha) }.$$ The radius of the pendulum’s center of mass is $R_{cm}$ (from its pivot) and the angle $\theta_{sb}$ is the angle set by the stop-bar from vertical. The speed of the marble when ejected from its holder is $$v_{eject} = L_m \dot \theta.$$ Here $L_m$ is the radial distance from the pivot to the center of the marble when it is in the launcher. The marble’s horizontal and vertical velocity components are $v_{x,eject} = v_{eject} \cos \theta_{sb} $ and $v_{z,eject} = v_{eject} \sin \theta_{sb} $.

We correct for the distance of projectile free fall before hitting the substrate surface, even though this correction is usually small. After it is ejected, the marble freely falls a distance of $$dz = L + d_{base} - d_s - L_m \cos\theta_{sb}$$ to hit the sand, where $d_s$ is the height of sand surface above the pendulum mechanism base. The estimated velocity of projectile impact with the sand substrate is $$v_{impact} = \sqrt{v_{z,eject}^2 +  2 g dz +  v_{x,eject}^2}
    