Nine rings, nine distances, one launch. Every problem randomizes the muzzle speed, the launch angle, and the muzzle height, so work out where each ring belongs before you fire. There are no practice shots.

How it works

You are given the muzzle speed, the launch angle, and the height of the muzzle above the bench. Derive the trajectory as a function of horizontal distance, then compute the height of each of the nine rings, measured from the bench surface to the center of the ring.

The rings are 12 cm across. The marble passes cleanly if your height is within 4.5 cm of the truth, and clips the rim out to 6.0 cm. You can drag a ring to set it roughly, but dragging will not land the far stations — only calculation will. The trajectory stays hidden until you launch.

Adapted from the Projectile Motion Hoop Challenge by C. Jordan, A. Dunn, Z. Armstrong, and W. K. Adams, The Physics Teacher 56, 200–202 (April 2018), and the PHYS 220 lab sheet behind it.