Solve For Y 2E8F7C

1. **State the problem:** We need to express $y$ as the subject of the formula from the equation $$2E = m(v^2 - y^2)$$. 2. **Write down the formula and rules:** The goal is to isolate $y$ on one side of the equation. We will use algebraic operations such as addition, subtraction, division, and taking square roots. 3. **Isolate the term containing $y^2$:** $$2E = m(v^2 - y^2)$$ Subtract $m v^2$ from both sides: $$2E - m v^2 = -m y^2$$ 4. **Divide both sides by $-m$ to solve for $y^2$:** $$\frac{2E - m v^2}{-m} = y^2$$ Show cancellation: $$y^2 = \frac{\cancel{2E} - \cancel{m} v^2}{-\cancel{m}} = \frac{m v^2 - 2E}{m}$$ 5. **Take the square root of both sides to solve for $y$:** $$y = \pm \sqrt{\frac{m v^2 - 2E}{m}}$$ 6. **Final answer:** $$y = \pm \sqrt{v^2 - \frac{2E}{m}}$$ This means $y$ is equal to plus or minus the square root of $v^2$ minus $\frac{2E}{m}$. This completes the solution.