NB! Problem 3 remains open for two more weeks, until 1st March, 23:59 GMT, but this is the last hint – there will be no more hints.
In order to solve the Problem 3 using the theorem of the Hint 3, answer first the following questions.
- Suppose the ball departs from its initially circular trajectory at point A, and henceforth starts moving along a parabolic trajectory (until meeting again the circle at a point B). The curvature radius of the circular trajectory is obviously l. Based on the laws of dynamics, what can be said about the curvature radius of the parabolic trajectory at the point A?
- The theorem of the Hint 3 is valid if a parabola intersects a circle at four points. Let us imagine moving the parabola while keeping the circle at rest until three intersection points merge into a single point P. What can be said about the curvature radius of the parabola at the point P?