Final answer:
The horizontal component of the force vector is approximately 259.8 pounds, and the vertical component is approximately 150 pounds. These components are calculated using trigonometric functions cosine and sine for a force that makes a 30° angle with the ground.
Step-by-step explanation:
A wagon is being pulled by a 300-pound force that makes a 30° angle with the ground. To find the horizontal and vertical components of this force vector, we can use trigonometry.
The horizontal component (Fx) can be found using the cosine function:
Fx = F × cos(θ)
For a 300-pound force at 30°:
Fx = 300 pounds × cos(30°)
Fx ≈ 300 pounds × 0.866 ≈ 259.8 pounds
The vertical component (Fy) can be found using the sine function:
Fy = F × sin(θ)
For a 300-pound force at 30°:
Fy = 300 pounds × sin(30°)
Fy ≈ 300 pounds × 0.5 ≈ 150 pounds
So, the horizontal component of the force is approximately 259.8 pounds and the vertical component is approximately 150 pounds.