# Projectile Motion Equation Need Help Re-arranging Please!

1. Mar 2, 2009

### AudioGeek

Hey, this is my first time posting here, I just found this site in a Google search.

I've been doing a projectile motion question, and I know what I am doing and solving for and such, but I am having great difficulties re-arranging the equation I need. The equation looks like so:
$$\Delta$$d$$_{}y$$ = v$$_{2y}$$$$\Delta$$t + $$\frac{1}{2}$$g$$\Delta$$t$$^{2}$$

The variable I need to solve for is time ($$\Delta$$t), but I'm having vast difficulties in doing so. I know I've solved this before, but am not entirely sure how I did it. If this makes no sense, I will post the whole question so I can be told what I'm doing wrong.

Thanks in advance for the help, I would really appreciate it!

EDIT: I think I'm doing this posting thing all wrong...sorry for my noob-ness.

Ninjaedit: the speed shouldn't be squared, it should be v2 (as in second) y...subscript doesn't work for me properly apparently

EDIT AGAIN: Okay, so in reading around a little bit more, I noticed I should list what I went through to try to rearrange this equation.
1. $$\Delta$$d$$_{}y$$ - v$$_{2y}$$$$\Delta$$t = $$\frac{1}{2}$$g$$\Delta$$t$$^{2}$$
2. $$\frac{$$\Delta$$d$$_{}y$$ - v$$_{2y}$$$$\Delta$$t}{0.5g}$$ = $$\Delta$$t$$^{2}$$

And that's where I got stumped. How would I isolate this variable? Is it do-able?

Last edited: Mar 2, 2009
2. Mar 2, 2009

### Nabeshin

'Ello, and welcome to PF!

In general, the solution to this is a quadratic which, depending on your math background, can look really sticky or really neat. If you re-write the equation like this:
$$\frac{1}{2}g\Delta t^{2}+v_{2y}\Delta t - \Delta d_{y}=0$$
You can see it's in the form of a quadratic...
$$at^{2}+bt+c=0$$

And I'll assume you're familiar with the quadratic formula...

Edit:

There is a special case of this when $$\Delta d_{y}=0$$ which isn't a quadratic (well it is, but one solution is always t=0).

3. Mar 2, 2009

### AudioGeek

Aaah, thank you very much for the reply! And yes, I am familiar with the Quadratic Formula, but haven't used it in a year. I made the mistake of stopping math at Grade 11 U level, in the same semester as my Grade 11 U Physics, and then taking Grade 12 U Physics, after having no math for a year.

tl;dr what's the Quadratic equation again?

Thanks again!

EDIT: Nvm, got it, thanks!