Velocity vector along a parabola

[matatat]

Hello, I'm new here and wasn't sure if this should be put into the homework section. It's not a homework question but the nature of the problem is homework-ish in nature I suppose.

Anyway I'm trying to understand why a velocity vector along a parabola would have the same initial velocity as its final velocity. I realize that velocity along the x-axis is a constant and I think the velocity along the y-axis remains linear. Although I can't figure out why both are so. Could someone explain this to me or direct me to where I would find the answer?

thanks
matt

 

[matatat]

Sorry also I forgot to mention that it makes sense in the fact that it will have enough velocity to reach a point y and its velocity will be zero and as it returns its velocity will return back to the original but negative. I was more so wondering how I could prove this with kinematics.

 

[Nabeshin]

I assume you're talking about a projectile thrown upwards in a gravitational field, right?

Then the behavior you describe is derived directly from Newton's second law. Namely, the gravitational force only acts in the -y direction. Can you see why this leads to the velocity relationships?