A vector is $25.6 \mathrm{~m}$ long and makes an angle of $60.0^{\circ}$ counterclockwise from the $y$-axis (on the side of the $-x$-axis).
What is the $x$-component of this vector?

Answer

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Answer

$x$-component = \boxed{22.17 \text{ m}}\)

Steps

Step 1 ：Find the angle the vector makes with the x-axis: $90^\circ - 60^\circ = 30^\circ$

Step 2 ：Calculate the x-component using the cosine of the angle and the length of the vector: $25.6 \times \cos(30^\circ)$

Step 3 ：$x$-component = $25.6 \times 0.866025$

Step 4 ：$x$-component = \boxed{22.17 \text{ m}}\)