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A vector is 4.0 cm long and makes an angle of 30° clockwise the X and y-components of this vector?

User Jschmier
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Final answer:

The X and Y components of a vector that is 4.0 cm long and makes a 30° clockwise angle from the X-axis are 3.46 cm and -2.0 cm, respectively.

Step-by-step explanation:

To determine the X and Y components of a vector that is 4.0 cm long and makes an angle of 30° clockwise from the X-axis, you can use trigonometric functions. The X component is found by multiplying the vector's length by the cosine of the angle, while the Y component is found by multiplying the vector's length by the sine of the angle. However, since the angle is clockwise, the Y component will be negative. Therefore:

  • X component (Ax) = 4.0 cm × cos(30°) = 4.0 cm × (√3/2) = 3.46 cm
  • Y component (Ay) = -4.0 cm × sin(30°) = -4.0 cm × (1/2) = -2.0 cm

The X component of the vector is 3.46 cm, and the Y component is -2.0 cm.

User Eliseo
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