In this problem, we are required to rotate the coordinate system and resolve a vector into its components.

2D vector Components:

$\overline{)\begin{array}{rcl}{\mathbf{v}}_{\mathbf{x}}& {\mathbf{=}}& \mathbf{\left|}\stackrel{\mathbf{\rightharpoonup}}{\mathbf{v}}\mathbf{\right|}\mathbf{}\mathbf{cos}\mathbf{}\mathbf{\theta}\\ {\mathbf{v}}_{\mathbf{y}}& {\mathbf{=}}& \mathbf{\left|}\stackrel{\mathbf{\rightharpoonup}}{\mathbf{v}}\mathbf{\right|}\mathbf{}\mathbf{sin}\mathbf{}\mathbf{\theta}\end{array}}$

The figure depicts the sum of two velocities

Part (a) Find the component, in meters per second, of v_{tot} along an x’-axis rotated 30° counterclockwise relative to the x-axis in the figure.

v_{tot x’}=

Part (b) Find the component, in meters per second, of v_{tot} along a y’-axis rotated 30° counterclockwise relative to the y-axis in the figure

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What scientific concept do you need to know in order to solve this problem?

Our tutors have indicated that to solve this problem you will need to apply the Vector Composition & Decomposition concept. You can view video lessons to learn Vector Composition & Decomposition. Or if you need more Vector Composition & Decomposition practice, you can also practice Vector Composition & Decomposition practice problems.