Question

a man is pulling a rope attached to a rock on a sloped road, exerting 200 pounds of force on the rope . If he is pulling at an angle of 45 with the horizontal and the slope of the road is 15 from the horizontal find the work done to pull the rock 100 feet

Answer 1

For a better understanding of the answer please find the diagram in the attachment.

As can be clearly seen from the diagram that the distance, "d" (shown in dark blue) of 100 feet which is covered on the sloped/inclined road is actually making an angle of only 30 degrees with the force of 200 pounds which is being applied on the road. That angle of 30 degrees is what matters.

So, the force, F=200 pounds

distance, d=100 feet

And the angle between the force, F and the distance, d is: $\theta=30^{\circ}$

Therefore, as per formula, the work, W, done will be:

$W=F\times d\times cos(\theta)$

This, when applied to the question we have will give us:

$W=200\times 100\times cos(30^{\circ})\approx17320.51 lb-ft$