Here's a problem I was doing.
A ball bearing, $A$ of mass $450g$ is thrown vertically down with a speed of $4{ms}^{-1}$ from a height of $2m$. It bounces back and just reaches it's original height. Find the coefficient of restitution between $A$ and the ground. Take $g$ to be $10{ms}^{-2}$.
Here is my working out:
Taking down to be positive. Finding the speed of approach:
$v^{2} = 4^{2} + 2(10)(2)$
$v^{2} = 56$ so $v = \sqrt{56}$
Then, to find speed of separation,
$ 0 = u^{2} +2(-10)(-2)$
But there's the problem. I won't be able to get $u$ on its own because I can't square root a negative number. I used $g = -10{ms}^{-2}$ here because now the ball is moving up (against down, which is +ve), and displacement is $-2m$ since the ball is moving up as well. But if I make one of them positive, I get speed of separation = $\sqrt{40}$ and so I can calculate the correct value of $e$.
The value of g is independent of the direction the ball is moving. If you took the downward direction to be positive, then g should be used with a positive sign in your equation. This is why you got a negative value for $u^2$.