How Do You Solve for Final Velocity in the Energy Equation Without Mass?

[Matt_AMG]

The question I have is trying to solve the final velocity in an energy equation that goes like this: 0.5mv^2=0.5mv^2+mgy (The final velocity being on the LS).

I'm not given the mass of the skier going down the hill so I divide to cancel the mass out. I then rearrange to get Vf^2 = V^2+gy. I've pretty much nailed it down to a simple algebra problem but I can't see what's wrong!

Oh, I might add that I always plug numbers in before rearranging equations but my teacher doesn't like me doing that.

 

[PhanthomJay]

The question I have is trying to solve the final velocity in an energy equation that goes like this: 0.5mv^2=0.5mv^2+mgy (The final velocity being on the LS).

I'm not given the mass of the skier going down the hill so I divide to cancel the mass out. I then rearrange to get Vf^2 = V^2+gy. I've pretty much nailed it down to a simple algebra problem but I can't see what's wrong!

Oh, I might add that I always plug numbers in before rearranging equations but my teacher doesn't like me doing that.

You canceled out the 'm's' just fine, but what you're left with is
$$0.5V_f^2 = 0.5V_o^2 + gy$$ you left out that 0.5 factor.
BTW, I always plug in numbers before rearranging equations. It sometimes leads to round off errors, but it sure makes the algebra a lot simpler and less confusing, because it's generally much easier to deal with numbers rather than letters, but don't tell teacher I said that!