# Problem: Vector A is in the direction 34.0° clockwise from the −y-axis. The x-component of A is Ax = −16.0 m.(a) What is the y-component of A?(b) What is the magnitude of A?

###### FREE Expert Solution
89% (185 ratings)
###### FREE Expert Solution

We're asked to determine the y-component and magnitude of a vector given its direction and x-component.

For any problems that ask us to relate the magnitude, angle, and components of a vector, there are two basic equations we'll use:

$\overline{)\mathbf{|}\stackrel{\mathbf{⇀}}{\mathbf{A}}\mathbf{|}{\mathbf{=}}\sqrt{{{\mathbf{A}}_{\mathbf{x}}}^{\mathbf{2}}\mathbf{+}{{\mathbf{A}}_{\mathbf{y}}}^{\mathbf{2}}}}$ (1)

$\overline{){\mathbf{tan\theta }}{\mathbf{=}}\frac{{\mathbf{A}}_{\mathbf{y}}}{{\mathbf{A}}_{\mathbf{x}}}}$ (2)
where θ is the angle of the vector measured counterclockwise from the +x-axis. (Counterclockwise is the standard positive direction for angles.)

It's also a good idea to sketch the problem so you can more easily visualize it.

89% (185 ratings) ###### Problem Details

Vector A is in the direction 34.0° clockwise from the −y-axis. The x-component of A is Ax = −16.0 m.
(a) What is the y-component of A?
(b) What is the magnitude of A?

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