Vector R has a magnitude of 36 units directed 30˚ from the +y – axis of a Cartesian plane. What are the x- and y-components of the vector?
Question
Vector R has a magnitude of 36 units directed 30˚ from the +y – axis of a Cartesian plane. What are the x- and y-components of the vector?
Solution
To find the x- and y-components of the vector, we can use the trigonometric functions sine and cosine.
The x-component of the vector is given by Rcos(θ), and the y-component is given by Rsin(θ).
Here, R is the magnitude of the vector (36 units), and θ is the angle from the +y-axis (30 degrees).
However, since the vector is directed from the +y-axis, we need to adjust the angle for the calculations. The angle from the +x-axis (which is the standard reference axis) is 90 degrees - 30 degrees = 60 degrees.
So, the x-component of the vector is Rcos(60) = 36cos(60) = 18 units.
The y-component of the vector is Rsin(60) = 36sin(60) = 31.18 units.
So, the x- and y-components of the vector are 18 units and 31.18 units, respectively.
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