Final answer:
The horizontal component (Fx) of the force is approximately 25.98 lb and the vertical component (Fy) is 15 lb, calculated using trigonometric functions with a 30 lb force at a 30° angle to the ground.
Step-by-step explanation:
To determine the horizontal and vertical components of a force exerted at an angle to the ground, you can use trigonometric functions like sine and cosine. In the case of a 30 lb force applied at a 30° angle to the ground, you would find the horizontal component (Fx) by multiplying the force by the cosine of the angle, and the vertical component (Fy) by multiplying the force by the sine of the angle.
Calculation steps:
Horizontal component (Fx): Fx = 30 lb × cos(30°)
Vertical component (Fy): Fy = 30 lb × sin(30°)
Using the trigonometric values:
cos(30°) ≈ 0.866
sin(30°) ≈ 0.5
The components would be:
Fx = 30 lb × 0.866 ≈ 25.98 lb
Fy = 30 lb × 0.5 = 15 lb
Therefore, the horizontal component of the force is approximately 25.98 lb, and the vertical component is 15 lb.