There is a common fact about projectile motion. Let me remind you with an example: Assume that you are aiming at a hanging banana on a tree. If there were no gravitational force, the bullet would follow a linear path at a time "t". But since it does exist such kind of force, a parabolic path will occur. Now suppose that the banana suddenly began to free fall at the exact moment when you fired the gun -again with aiming at the banana's initial position. You will hit the banana literally. That is, the elapsed time for the free-fall of the banana and the projectile motion of the bullet are the same and equal to the certain "t" as stated above. Now my question is, how can we proof that with motion in 2D formulas?
(Banana is y meters above the ground. The diagonal distance between the shooter and the banana is z meters, also the shooter is x meters to the left for banana horizontally and they collide each other when the banana has already traveled over h meters.)