Given the displacement 19 m, 310 South of West. What is the x-component of the displacement? Input a value in two decimal places.
Question
Given the displacement 19 m, 310 South of West. What is the x-component of the displacement? Input a value in two decimal places.
Solution
The x-component of the displacement can be found using trigonometry.
The displacement vector makes an angle of 310 degrees with the positive x-axis (East). However, since we are considering South of West, we need to convert this to an angle with respect to the West direction (negative x-axis). This gives us an angle of 310 - 180 = 130 degrees.
The x-component of the displacement is given by the magnitude of the displacement times the cosine of the angle. In this case, the magnitude of the displacement is 19 m and the angle is 130 degrees.
So, the x-component of the displacement is -19 * cos(130) = -19 * (-0.6428) = 12.21 m.
Therefore, the x-component of the displacement is 12.21 m.
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