What would it take?
By my calculations the riders in the capsule would experience 22,000g of acceleration on their way out of a mountain size barrel of the cannon, and neglecting air resistance would hit the ground at the exact same speed it left. This speed being roughly 115,200 miles per hour. These numbers are by no means small and would take a huge force to generate that acceleration. The Newtons required would be literally astronomical. Then assuming no deformation in the shell from hitting an ocean for landing, and that the shell would submerge 1 mile under water before coming to rest and returning to the surface the riders would feel a deceleration of roughly 824,000m/s^2.