"Slippery Slope" - a Parametric Trajectory problem

Question

I'm designing some equipment that spits out a small ball, which I want to capture when it lands, without it bouncing away. I figure this can be done by having the ball strike a slope tangentially. I define the problem as:

"A particle P subject to earth's gravity leaves a launch point (0,k) at positive velocity V in both the x and y direction. Is there a slope S, lying below and to the right of k, such that for any V, the particle hits S tangentially ? If so, express Sy as a function of Sx"

Diagram shows x and y axes (black), Particle P's initial velocity vectors (red), and subsequent parabolic motion (blue, depending on V). Curve S (green) is formed when P glances tangentially regardless of V.

Forming the parametric equations for Px and Py as functions of t (time) is simple. Px and Py can then be expressed as functions of V. Conceptually, the constraint that the slope of S equals the slope of P at the point of impact should be incorporated as a constraint, but not sure how to do this.

Appreciate all assistance