Question

vectors
physics: vector addition worksheet i
name:
date:
find the x and y components of each of the following vectors.

Explanation:

Step1: 分解12m向量

根據向量分解公式\(A_x = A\cos\theta\)，\(A_y = A\sin\theta\)（\(A\)為向量大小，\(\theta\)為與\(x\)軸夾角）。
對於\(12m\)向量，\(x\)分量\(x_1 = 12\cos30^{\circ}=12\times\frac{\sqrt{3}}{2}=6\sqrt{3}m\)，\(y\)分量\(y_1 = 12\sin30^{\circ}=12\times\frac{1}{2}=6m\)。

Step2: 分解25m/s向量

同樣根據向量分解公式。
\(x\)分量\(x_2 = 25\cos60^{\circ}=25\times\frac{1}{2}=12.5m/s\)，\(y\)分量\(y_2 = 25\sin60^{\circ}=25\times\frac{\sqrt{3}}{2}=\frac{25\sqrt{3}}{2}m/s\)。

Answer:

\(12m\)向量：\(x = 6\sqrt{3}m\)，\(y = 6m\)；\(25m/s\)向量：\(x = 12.5m/s\)，\(y = \frac{25\sqrt{3}}{2}m/s\)。