Question

a force of 50 pounds acts in a direction 60° above horizontal, moving an object 100 feet from (0, 0) to (100, 0). how much work is done by the force? 25 foot - pounds 50 foot - pounds 2,500 foot - pounds 5,000 foot - pounds

Explanation:

Step1: Recall the work formula

The formula for work \(W=\vec{F}\cdot\vec{d}=\vert\vec{F}\vert\vert\vec{d}\vert\cos\theta\), where \(\vert\vec{F}\vert\) is the magnitude of the force, \(\vert\vec{d}\vert\) is the magnitude of the displacement, and \(\theta\) is the angle between the force and displacement vectors.

Step2: Identify the values

Given \(\vert\vec{F}\vert = 50\) pounds, \(\vert\vec{d}\vert=100\) feet, and \(\theta = 60^{\circ}\).

Step3: Calculate \(\cos\theta\)

We know that \(\cos60^{\circ}=\frac{1}{2}\).

Step4: Substitute values into the formula

$$
LATEXBLOCK0
$$

So the work done by the force is \(2500\) foot - pounds.

Answer:

C. 2,500 foot - pounds