Question

review the diagram.
a wagon is being pulled by a 300 - pound force that makes a 30° angle with the ground. what are the horizontal and vertical components of the force vector?
the horizontal is 150 pounds, and the vertical is 260 pounds.
the horizontal is 260 pounds, and the vertical is 150 pounds.
the horizontal is 346 pounds, and the vertical is 600 pounds.
the horizontal is 600 pounds, and the vertical is 346 pounds.

Explanation:

Step1: Calculate horizontal component

The formula for the horizontal component \(F_x\) of a force \(F\) at an angle \(\theta\) is \(F_x = F\cos\theta\). Given \(F = 300\) pounds and \(\theta=30^{\circ}\), then \(F_x=300\cos30^{\circ}\). Since \(\cos30^{\circ}=\frac{\sqrt{3}}{2}\approx0.866\), \(F_x = 300\times0.866 = 259.8\approx260\) pounds.

Step2: Calculate vertical component

The formula for the vertical component \(F_y\) of a force \(F\) at an angle \(\theta\) is \(F_y = F\sin\theta\). Given \(F = 300\) pounds and \(\theta = 30^{\circ}\), then \(F_y=300\sin30^{\circ}\). Since \(\sin30^{\circ}=\frac{1}{2}\), \(F_y=300\times\frac{1}{2}=150\) pounds.

Answer:

B. The horizontal is 260 pounds, and the vertical is 150 pounds.