Projectile motion

[BlackFrost]

Hey guys,
Could someone explain why the magnitude of the initial vertical velocity is the same as the final vertical velocity (instant before it falls onto the ground). Some sites said something about parabolic trajectory, but I couldnt really understand what that means. Thanks.

[Bri MT]

Hey,

When we do these questions we ignore air resistance. Vertically, we have constant acceleration due to gravity. This is acting in the opposite direction to the initial vertical velocity until eventually we hit the vertical component of the speed being 0 at the peak of the height.  If the projectile is landing at the same height then the trip down you have the same distance, same acceleration, it's going to take the same amount of time and your change in velocity is going to have the same magnitude. This time, you started at zero so that change in speed from the peak down is going to get you to the speed you initially started at.

If the projectile does not land at the same height it was launched from, you do not get a symmetrical flight & the final speed will be different to the initial speed.

Hope this helps