Question

Find the x and y components for the vector shown that is 25 units long and 53.1 degrees above the x-axis.

Answer 1

Given,

The length of the vector, V=25 units.

The angle of the vector, θ=53.1°

The x-component of the vector is given by,

`V_x=V\cos \theta`

On substituting the known values,

`\begin{gathered} V_x=25*\cos 53.1^(\circ) \\ =15.01\text{ units} \\ \approx15\text{ units} \end{gathered}`

The y-component of the vector is given by,

`V_y=V\sin \theta`

On substituting the known values,

`\begin{gathered} V_y=25*\sin 53.1^(\circ) \\ =19.99\text{ units} \\ \approx20\text{ units} \end{gathered}`

Thus, the x-component of the vector is 15 units and the y-component of the vector is 20 units.