How Do Final Speeds of Two Balls Compare When Thrown from a Building?

[aquapod17]

Homework Statement

A student at the top of a building of height h throws ball 1 upward with a speed of v_i and then throws ball 2 downward with the same initial speed, v_i. How does the final speed of ball 1, v_1f, compare to the final speed of ball 2, v_2f, when they reach the ground?
v_1f = ______ multiplied by v_2f

Homework Equations

a = delta v/delta t
v_f = v_i + a(delta t)

The Attempt at a Solution

I drew a picture showing the person throwing ball 1 upward and then it descending and ball two falling to the ground.

 

[Rake-MC]

Okay well let's think about this. We know if there is presence of uniform force in only one dimension then the trajectory is going to be parabolic. For ball 1, it will leave his hand at v_i go up in its arc, reach a maximum height (where vertical velocity is zero) begin to fall again with identical acceleration as before.
This implies that when it passes the thrower for, it will have the same velocity it was thrown with, but in the opposite direction.