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?

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}}\)