4. A rectangular swimming pool is 100 ft wide, 200 ft long, and 6 ft deep. The pool is filled to a depth of 5 ft with water. Assume the water must be pumped to the top of the pool deck, which is at the top edge of the pool. The density of water is approximately 62.4 lb/ft³.
1. Calculate the total work required to pump all the water out of the pool.
2. Provide all necessary steps, including the integral setup and evaluation.
5. The velocity of a car after t seconds is $75-3t^2$ feet per second. (a) How many seconds does it take for the car to come to a stop (velocity= 0)? (b) How far does the car travel while coming to a stop? (c) How many seconds does it take the car to travel half the distance in part (b)?
6. A circular window on a submersible vessel has a diameter of 5 ft and is submerged in seawater. The center of the window is located 500 ft below the surface. The density of seawater is approximately 64 lb/ft³.
1. Find the total fluid force exerted on the window.
2. Provide all necessary calculations, including the integral setup and evaluation.
