A ball is launched from a level floor with speed $v$ at angle $\theta$ above the horizontal, inside a hall whose flat ceiling sits at height $h$ above the floor. The launch is steep enough that the ball strikes the ceiling, i.e. $v^2 \sin^2\theta > 2gh$. The ceiling is perfectly elastic, the floor is perfectly absorbing on the second floor contact, and only gravity acts during flight. How far horizontally from the launch point does the ball first land back on the floor?