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I want to write a projectile motion question where a spherical ball is launched from the ground with, say, initial velocity $ v $ (applied to the center of the ball) and angle of projection $ \theta $, which then passes through a hole in a ramp inclined at an angle $ \alpha $ to the horizontal. The hole is the same size as the ball so it will just make it through, as shown below. Diagram I just need to know, does the tangent to the parabola (that represents the path of the trajectory) necessarily have to be perpendicular to the ramp at the point where the center of the ball coincides with the center of the hole? Is this always true, sometimes true, or never true?

Thanks in advance.

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  • $\begingroup$ Tilting the ramp relative to the direction of the ball’s velocity effectively makes the hole narrower. $\endgroup$ – amd Jul 13 '18 at 19:34

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