Final answer:
The force of the water on the dam is approximately 2,457,600 lb.
Step-by-step explanation:
In this problem, we can calculate the force on the dam using the formula F = pgh²L/2, where p is the density of water, h is the depth of the water at the dam, and L is the length of the dam.
To find the force of the water on a dam, we can use the formula F = pgh²L/2, where p represents the density of water, g is the acceleration due to gravity, h is the depth of the water at the dam, and L is the length of the dam. The dam in question has a length of 98 ft, and the water has a depth of 40 ft. Given the density of water is 62.4 lb/ft³, the force exerted on the dam is calculated as follows:
Given that the density of water is 62.4 lb/ft³, the depth is 40 ft, and the length is 98 ft, we can substitute these values into the formula:
F = (62.4 lb/ft³) × (40 ft)² × (98 ft) / 2
Calculating this gives us F ≈ 2,457,600 lb.
Therefore, the force of the water on the dam is approximately 2,457,600 lb (Option A).