A 1,160-N crate is being pushed across a level floor at a constant speed by a force vector F of 310 N at an angle of 20.0° below the horizontal, as shown in the figure (a) below.

Incomplete.

To find the horizontal and vertical components of the force vector, we can use trigonometry.

The horizontal component (Fx) can be found using the equation Fx = F * cos(theta), where F is the magnitude of the force vector and theta is the angle below the horizontal.

Given:
F = 310 N
theta = 20.0°

Using the equation:
Fx = 310 N * cos(20.0°)
Fx = 310 N * 0.93969
Fx ≈ 290.7 N

So, the horizontal component of the force vector is approximately 290.7 N.

Now, let's find the vertical component (Fy) using the equation Fy = F * sin(theta).

Using the equation:
Fy = 310 N * sin(20.0°)
Fy = 310 N * 0.34202
Fy ≈ 105.9 N

So, the vertical component of the force vector is approximately 105.9 N.

Therefore, the horizontal component of the force vector is 290.7 N (to the right) and the vertical component is 105.9 N (downwards).