Projectile Motion is Symmetric

[Bashyboy]

Okay, I read that in the case of no air-resistance, projectile motion is symmetric; that the initial velocity will equal the final velocity, in magnitude; and that a projectile traveling upwards, achieving a zero velocity of the vertical component, will have to fall the same horizontal distance during the segment of motion downwards. But, for some odd reason, I just have difficulty grasping this. Is there something I am missing in my understanding? Is there a better way to explain this concept?

 

[DragonPetter]

Okay, I read that in the case of no air-resistance, projectile motion is symmetric; that the initial velocity will equal the final velocity, in magnitude; and that a projectile traveling upwards, achieving a zero velocity of the vertical component, will have to fall the same horizontal distance during the segment of motion downwards. But, for some odd reason, I just have difficulty grasping this. Is there something I am missing in my understanding? Is there a better way to explain this concept?

I think one way that might help is to understand all of this motion is with relation to time. If something is moving at a constant velocity in the horizontal direction, and it moves in the positive vertical direction for time t, then it will move in the negative direction for time t also. So, if horizontal velocity is constant, and time t up is equal to time t down, then the horizontal distances going up must be the same as down.