# Defying Gravity! - 4-sided

This is an extension of this problem.

Now, imagine four surfaces of equal length making a square in a controlled environment, with same parameters (the gravity can be switched to be perpendicular to any of the surfaces). Now, say a ball is dropped from the midpoint of one of the sides of the square, falling in direction perpendicular to the adjacent side of the square. After a certain time period $$t_1$$, the direction of the acceleration due to gravity is switched in a cyclic manner, to the next adjacent surface. Then, after time $$t_2$$, the direction is switched in the same fashion. Then after every time period $$T$$, the direction of gravity is changed. The periodic changes occur in such a way that the ball visits the midpoints of all four surfaces. If the surfaces are $$1 km.$$ long, and the acceleration due to gravity is $$10 ms^{-2}$$, find $$\lfloor t_2-t_1\rfloor$$.

Also, derive the expression for $$T$$, in terms of $$k$$ and $$g$$, which are length of surface and acceleration due to gravity respectively.

×