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Problem: Vector A has y-component Ay = +15.0 m and makes an angle of 32.0° counterclockwise from the +y-axis.(a) What is the x-component of A?(b) What is the magnitude of A?

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FREE Expert Solution

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

A=Ax2+Ay2 (1)

tanθ=AyAx (2)
where θ is the angle of the vector measured counterclockwise from the +x-axis. (By convention, counterclockwise is the positive direction for angles.)

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

(a) For this part of the problem, we're asked to determine the x-component of the vector, Ax. We're given the vector's y-component (Ay = +15.0 m) and the angle it makes with the +y-axis, in the counterclockwise direction.

Since the given angle isn't measured from the +x-axis, we'll need to determine what our θ is. It's in Quadrant 2, which means that if we want it as a positive angle, θ should be between 90° and 180°:

θ=90°+32°=122°

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Problem Details

Vector A has y-component Ay = +15.0 m and makes an angle of 32.0° counterclockwise from the +y-axis.

(a) What is the x-component of A?
(b) What is the magnitude of A?

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