问题103: A person going for a walk follows the path shown in the pict

A person going for a walk follows the path shown in the picture below. The total trip consists of four straight-line paths.
What is the magnitude of person's resultant displacement measured from the starting point. The magnitudes of the vectors are: $A_1=96 m , A_2=371$ $m , A_3=139 m$, and $A_4=236 m$.

已解决 · 高中数学位移 · 平面向量
提问于1月18日 · 阅读 288

解答

这四步的向量如下:

$$ \begin{aligned} & (96,0) \\ & (0,-371) \\ & -\left(139 \cdot \frac{\sqrt{3}}{2}, 139 \cdot \frac{1}{2}\right) \\ & \left(236 \cdot\left(-\frac{1}{2}\right), 236 \cdot \frac{\sqrt{3}}{2}\right) \end{aligned} $$

相加后得到:

$(-\frac{139 \sqrt{3}}{2}-22,118 \sqrt{3}-\frac{881}{2})$

从而位移的大小为

$\sqrt{\left(-\frac{139 \sqrt{3}}{2}-22\right)^2+\left(118 \sqrt{3}-\frac{881}{2}\right)^2}=275.723$

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