A vector is 21.8 m long and makes an angle of 58.9° counterclockwise from the y-axis (on the side of the -x-axis). What is the x-component of this vector?

The x-component of a vector can be found using the formula:

Vx = V * cos(θ)

where V is the magnitude of the vector and θ is the angle it makes with the positive x-axis. However, in this case, the angle is given with respect to the y-axis.

The angle with respect to the x-axis would be 90° - 58.9° = 31.1° (since the vector is on the side of the -x-axis, the angle is measured in the clockwise direction).

Now, we can substitute V = 21.8 m and θ = 31.1° into the formula:

Vx = 21.8 m * cos(31.1°)

Please note that the cosine function in most calculators requires the angle to be in radians. To convert from degrees to radians, multiply by π/180. So, 31.1° = 31.1 * π/180 radians.

Vx = 21.8 m * cos(31.1 * π/180)

Calculate the above expression to find the x-component of the vector. Since the vector is in the negative x direction, the x-component will be negative.