Final answer:
The total work done by the fireman in pulling up 200 ft of rope is calculated as the sum of an arithmetic series, resulting in 5050 ft-lb which is closest to option (d) 5,000 ft-lb, though none of the options precisely match.
Step-by-step explanation:
The total amount of work done in pulling the entire rope up to the top of the building can be calculated by considering the work done in lifting each segment of the rope from the ground to its final height. Since the rope weighs 1 lb/ft, for every foot of rope lifted, the work done is equivalent to the weight of the rope times the distance it was lifted.
To find out the total work, we divide the rope into segments and calculate the work done on each segment. The fireman lifts the first foot of the rope by 100 feet, the second foot by 99 feet, the third foot by 98 feet, and so on until the fireman lifts the 100th foot of the rope by 1 foot.
The work done on each segment forms an arithmetic series with 100 terms. The sum of this arithmetic series is:
Work = (n/2) × (first term + last term) = (100/2) × (100 + 1) × 1 lb
Therefore, the total work done is:
Work = 50 × 101 × 1 = 5050 lb-ft
Since option (d) is 5,000 ft-lb and none of the options exactly match our calculation, the correct answer appears to be closest to choice (d), 5,000 ft-lb, but none of the options provided is exactly correct based on our detailed calculation.