Why Does a Ball Thrown Upwards Return at the Same Speed?

[quark001]

My high school physics textbook says that the speed at which a ball leaves your hand (when thrown upwards) is the same as the speed at which you catch it (if you don't move your hand). That means that the time for the ball's upwards movement is the same as for its downwards movement. Why is this?

 

[dikmikkel]

Moving up: The potential energy increases while the kinetic decreases(smaller velocity)
Down: The kinetic energy increases while the potential decreases.

So it is a matter of conservation of energy.