What does 'plus or minus' mean as it pertains to real word situations? I'm doing a lab for my AP Physics class where I have to derive an equation for velocity. Trouble is when I do I get a value for velocity that is ±. $$\pm \sqrt{g\cdot r\cdot cot(\Theta)}$$ In the past, I've ignored the + or - and just taken the +. I wonder though if that is okay? In real life situations, how can you mathematically decide on the + or the -? Edit: The lab specifically involves finding the velocity of a toy plane with a fan on the back producing thrust. The plane is attached to a string attached to the ceiling. The setup looks something like this. I solve for velocity by writing two equations for the tension ($T = \frac{mg}{sin(\Theta)}$ and $T = \frac{m\cdot v^{2}}{r\cdot cos(\Theta))}$) and solving for v.

When you solve the equation for the velocity of the plane you are really solving.. $$ v^2=\vec v \cdot \vec v = gr\cot\theta $$

This gives you the magnitude of $\vec v$ but says nothing about the direction.

Mathematically there is no way to determine this from the equation.

Physically I suspect that you assumed the velocity to be horizontal and perpendicular to the cable.

There is a real ambiguity about the sense of revolution, it could be either clockwise or counter-clockwise depending on initial conditions.