Physics Problem: Ball Rolling and Projectile Motion Combined

This content solves a multi-part physics problem involving a solid ball that first rolls smoothly along a horizontal path, then up a ramp onto a plateau, and finally launches horizontally to land at a specific distance. It demonstrates the application of kinematic equations for projectile motion to find initial velocity after launch and then uses the conservation of mechanical energy (including both translational and rotational kinetic energy) to determine the initial speed at which the ball must be shot.