Solve 1/2*m*v^2=m*g*h

$$\frac { 1 } { 2 } \cdot m \cdot v ^ { 2 } = m \cdot g \cdot h$$

Solve for g

$$\left\{\begin{matrix}g=\frac{v^{2}}{2h}\text{, }&h\neq 0\\g\in \mathrm{R}\text{, }&\left(v=0\text{ and }h=0\right)\text{ or }m=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Swap sides so that all variable terms are on the left hand side.

$$mgh=\frac{1}{2}mv^{2}$$

The equation is in standard form.

$$hmg=\frac{mv^{2}}{2}$$

Divide both sides by mh.

$$\frac{hmg}{hm}=\frac{mv^{2}}{2hm}$$

Dividing by mh undoes the multiplication by mh.

$$g=\frac{mv^{2}}{2hm}$$

Divide \frac{mv^{2}}{2} by mh.

$$g=\frac{v^{2}}{2h}$$

Solve for h

$$\left\{\begin{matrix}h=\frac{v^{2}}{2g}\text{, }&g\neq 0\\h\in \mathrm{R}\text{, }&\left(v=0\text{ and }g=0\right)\text{ or }m=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Swap sides so that all variable terms are on the left hand side.

$$mgh=\frac{1}{2}mv^{2}$$

The equation is in standard form.

$$gmh=\frac{mv^{2}}{2}$$

Divide both sides by mg.

$$\frac{gmh}{gm}=\frac{mv^{2}}{2gm}$$

Dividing by mg undoes the multiplication by mg.

$$h=\frac{mv^{2}}{2gm}$$

Divide \frac{mv^{2}}{2} by mg.

$$h=\frac{v^{2}}{2g}$$