# Defying Gravity!- 2-Sided

**Classical Mechanics**Level 3

Consider two surfaces parallel to each other in a controlled environment. The environment is made in such a way that the direction of the acceleration due to gravity can be flipped i.e. if the direction of gravity is perpendicular to one of the surfaces, the direction can be switched such that it is perpendicular to the other surface. Now, a ball is dropped from one of the surfaces, and falls to the other. However, after a certain time, the direction of acceleration is flipped, such that when the ball reaches the other surface, its velocity is zero. Then after every time period \(T\), the gravity is flipped such that the ball continues to reach the surfaces with a velocity equal to zero. If the distance between the two surfaces is \(10\) \(m.\)and the acceleration due to gravity in the system is \(10\) \(ms^{-2}\), find time period \(T\).

Also, after solving, generalize a formula for the time period \(T\) for the surfaces at distance \(k\) apart, with acceleration due to gravity as \(g\)

Try a harder version of this problem!