Question

Is the initial velocity equal to final velocity in projectile motion?

Answer 1

No,

If you fire a projectile directly upwards (acceleration due to gravity), and if there is no wind resistance*, then the final speed is equal to the initial speed, however in the opposite direction. The final velocity is therefore the negative of the initial. I think this is where you are confused.

In the more general case even this is not true. Air resistance effects motion, causes frictional slowing and terminal velocity. The elevation of the final velocity might not be the same (e.g. shooting up a mountain) which would cause some of the energy to still be in potential form...etc.


*and we ignore the minor effects of the rotation of the Earth. Due to the rotation, the final location of the projectile would not be identical to its starting point, however the effect is very small normally.