NB! Problem 3 remains open for one more week, **until 1st March**, **23:59 GMT.** I promised the previous hint to be the last one, but seeing that there were only very few correct solutions submitted during the last week, so here is one more hint.

Notice that before the ball departs from its circular orbit, the circle’s radius need to be smaller than the curvature radius of the parabolic trajectory drawn from the given point, tangent to the circle. Indeed, otherwise the centripetal acceleration would be too small to keep the string taut. After the ball departs from its circular orbit, the circle’s radius need to be bigger than the curvature radius of the parabolic trajectory drawn from the given point tangent to the circle. Indeed, otherwise the centripetal acceleration would be too large for the string become slack. So, the curvature radius of the parabola equals to the radius of the circle at the point were the ball departs from the circular orbit. Now, you need to show that this means that three intersection points (introduced by the previous hints) merge into a single intersection point; use this fact to solve the problem (make use of the previous hints)!