Whakaoti i te E=1/2mv^2+mgh.quadv

$$E = \frac { 1 } { 2 } m v ^ { 2 } + m g h . \quad v$$

Whakaoti mō g

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

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

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

Tangohia te \frac{1}{2}mv^{2} mai i ngā taha e rua.

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

He hanga arowhānui tō te whārite.

$$hmg=-\frac{mv^{2}}{2}+E$$

Whakawehea ngā taha e rua ki te mh.

$$\frac{hmg}{hm}=\frac{-\frac{mv^{2}}{2}+E}{hm}$$

Mā te whakawehe ki te mh ka wetekia te whakareanga ki te mh.

$$g=\frac{-\frac{mv^{2}}{2}+E}{hm}$$

Whakaoti mō E

$$E=\frac{m\left(v^{2}+2gh\right)}{2}$$