ABOUT PHYSICS (momentum)

In fact, your answer of - 2 m/s has already indicated that it is in opposite direction to the rebound velocity, which is written as +0.5 m/s in your equation. Here, you have assumed the upward velocity (and force too) is positive and downward be negative.
為何rebounds的速度不用改變方向??
如 2 = 0.8 x (-0.5 - u )
This equation is wrong.
If you take upward as -ve, so that the rebound velocity is written as -0.5 m/s, then you also have to affix a -ve sign to the force, which is acting upward onto the water. That is - 2 N
The equation then becomes:
-2 = 0.8 x (-0.5-u)
i.e. -2 = -0.8 x (0.5+u)
or 2 = 0.8 x (0.5+u)
hence, u = +2 m/s (i.e. a downward velocity of 2 m/s)
BTW, in the equation 2 = 0.8 x (0.5 - u )/2, the division by 2 is rebundant. The correct equation should be 2 = 0.8 x (0.5 - u )

F (Force) and a (acceleration) are vectors. They have direction.
a = v - u where v: final velocity and u: initial velocity; Note that v and u are in the same direction as "a" is defined as acceleration.
It is about the assumption of the direction for all the vectors.
Now, the water is bounced backward and so it should be moving in the negative direction. In this situation, the water is moving in a negative direction against the pre-defined direction of v. By combining these two condition, the two negative sign for the direction canceled out each other.
It is a little trick playing with the vector direction.