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!

 

[m2003]

I would first like to commend you for your approach to solving this problem. It is important to understand the equations and principles involved before plugging in numbers. In this case, the energy equation you have written is correct and can be rearranged to solve for the final velocity.

However, I believe the issue may lie in the fact that the mass of the skier is not given. In order to solve for the final velocity, we need to know the initial velocity, the height of the hill (represented by "y" in the equation), and the mass of the skier. Without the mass, we cannot accurately determine the final velocity.

I would suggest going back to your teacher and asking for the mass of the skier or clarifying if it is meant to be left out of the problem. Without this information, it is not possible to solve the equation for the final velocity.

Additionally, I would recommend always checking your units when rearranging equations. In this case, the units on both sides of the equation should be in meters per second squared (m/s^2). If the units do not match, then there is likely an error in the equation or rearrangement.

Overall, your approach to the problem is correct, but without the necessary information, it is not possible to accurately solve for the final velocity. I hope this helps and good luck with your studies!