to get K2 + U2 = K1 + U1 and that's the conservation of energy.

可以得到能量守恒定律 K2 + U2 = K1 + U1
You want to try the same thing in two dimensions; that's your goal.

我们想要验证它是否适用于二维的情形
So, the first question is, "What should I use for the work done?"

首先要考虑怎么表示力所作的功
What expression should I use for the work done in two dimensions,

在二维里怎么来表示力所做的功呢
because the force now is a vector; force is not one number,

因为力是一个矢量而非标量
it's got an x part and a y part.

它既有 x 分量又有 y 分量
My displacement has also got an x part and a y part

而位移也同时有 x 分量和 y 分量
and I can worry about what I should use.

那我们就该考虑一下该怎么办了
So, I'm going to deduce the quantity I want to use for ΔW,

我们必须要算出 ΔW 的值
namely, the tiny work done which is an extension of this.

也就是所做的功这个的展开
I'm going to demand that since I'm looking for a Work Energy Theorem,

因为我想要推导出功能原理
I'm going to demand that,

我想要