How can I rearrange an equation to solve for v without using t?

[tomwilliam]

I've got a kinematics equation modelling the flight of a stone:

v = 10-gt
s= -1/2 g t^2 +10t +2

I can't remember how to get a value for v which doesn't contain t.
I tried rearranging the first equation and introducing it to replace t in the second, but can't seem to get v isolated:

(10-v)/g = t

s = -1/2 g ((10-v)/g)^2 + 10((10-v)/g) + 2

s = -1/2 ((10-v)^2/g) + (100-10v)/g + 2

but I can't work out how to get a single expression for v. Can anybody help?
This isn't a homework question, and I know the final solution is:
v=sqrt(4g+100-2gs)
It's just that I'm revising some stuff and really should know this already...!

 

[Petr Mugver]

Try using conservation of energy:

$$E=\frac{1}{2}mv^2+mgs=\textrm{initial value of E}$$

 

[jtbell]

It may not literally be a homework question, but it's a homework-like question, so it belongs here where it's been moved.

It might be easier if instead of solving the first equation for t and substituting into the second equation, you do it the other way around: solve the second equation for t and...

Do you remember how to solve a quadratic equation?

 

[tomwilliam]

Thanks for your reply.
I realize that I can calculate this using energy considerations...but is there not a way to do it using algebra alone? I'm reading through a maths textbook that gives these equations and simply says "rearranging the equations we can easily show that..." then gives the solution. As the textbook doesn't presuppose any physics background, I was trying to work out how to do it algebraically without invoking any physics principles.
Thanks

 

[tomwilliam]

Yes, sorry for posting in the wrong spot.

I've got it now...just a momentary blank.
Thanks for your help