A student realizes that a point particle that is able to rise at a given point P 0 at height H when
launched vertically from the origin O of a Cartesian plane at a fixed initial speed V 0 cannot
reach, by means of a direct shot from a small spring cannon, a point P positioned at the same height
H and distance d from P 0 , with 0 < d ≤ R , where R is the maximum horizontal distance attainable
with an optimum throw at an angle of 45°. However, the student realizes that, in the absence of air
resistance, conservation of energy does not prevent this possibility. Therefore, in order to reach
point P , the student uses a perfectly reflecting surface, opportunely inclined with respect to the
horizontal. The full story of how this is done will be narrated in this article.