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A velocity vector 30 ° above the positive x -axis has a y -component of 12 m/s. What is the value of its x -component?

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Final answer:

The x-component of the velocity vector is calculated using the y-component and the angle of the vector above the positive x-axis. By applying trigonometric identities, specifically the tangent function, the x-component is found to be approximately 20.78 m/s when the y-component is 12 m/s and the angle is 30°.

Step-by-step explanation:

The student is asking about the x-component of a velocity vector given the y-component and the angle above the x-axis. To find the x-component of a velocity vector when the angle and y-component are known, one would use trigonometry, specifically the cosine function since the y-component relates to the sine function. Assuming the velocity vector makes a 30° angle with the positive x-axis, and it has a y-component of 12 m/s, we can calculate the x-component (Ux) using the cosine function and trigonometric identities. The relationship we would use is:

Ux = Uy / tan(θ)

Given that Uy is 12 m/s and θ is 30°, we find

Ux = 12 m/s / tan(30°) = 20.78 m/s

Therefore, the x-component of the velocity is approximately 20.78 m/s.

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