Question

Break each of the following vectors into their x and y components

Answer 1

Given vectors,

`\begin{gathered} \vec{\Delta d}=50\text{ m}\lbrack S14\degree E\rbrack \\ \vec{v}=200\text{ m/s}\lbrack W30\degree S\rbrack \\ \vec{a}=15\text{ m/s }^2\lbrack E56\degree N\rbrack \end{gathered}`

Considering the vector Δd;

`\begin{gathered} \vec{\Delta d_x}=50*\sin 14\degree\hat{i} \\ =12.1\hat{i}\text{ m} \\ \vec{\Delta d_y}=50*\cos 14\degree(-\hat{j)} \\ =-48.5\hat{j}\text{ m} \end{gathered}`

Where Δd_x is the x component of the vector and Δd_y is the y-component of the vector.

Considering the vector v;

The x component of the vector is,

`\begin{gathered} \vec{v_x}=200*\cos 30\degree(-\hat{i}) \\ =-173.2\hat{i}\text{ m} \end{gathered}`

The y-component of the vector is,

`\begin{gathered} \vec{v_y}=200*\sin 30\degree(-\hat{j}) \\ =-100\hat{j}\text{ m/s} \end{gathered}`

Considering the vector a;

The x component of the vector is,

`\begin{gathered} \vec{a_x}=15\cos 56\degree\hat{i} \\ =8.4\hat{i}\text{ m/s}^2 \end{gathered}`

The y component of the vector is,

`\begin{gathered} \vec{a_y}=15\sin 56\degree\hat{j} \\ =12.4\hat{j}\text{ m/s}^2 \end{gathered}`