we may assert that (1/2)·m·v^2 + m·g,

我们可以说 (1/2)·m·v^2 + m·g
let me call it height instead of y,

我们用高度来代替 y
let me call this coordinate h instead of y;

用坐标 h 代替 y
I don't think it matters too much.

这没什么影响
That is the total energy and that is a constant.

这是总能量是个恒量
We applied it the other day to roller coasters,

我们曾把它应用于过山车问题
going up and down, speeding up and slowing down.

上下行驶加速减速
It's just that this number will not change.

但这个数值不会变
As the roller coaster changes the height,

随着过山车高度改变
the speed must change, keeping this number constant.

速度肯定改变以保持这个数为常量
But you know this formula is an approximation near the Earth.

但这个公式在近地表其实是个近似估算
You want to apply it globally.

我们要把它推广一下