At launch, a rocket weighing 2,500,000 lbs. carries a 200,000 lb. space shuttle. Assume that in the initial stages of launch, the rocket consumes fuel at a rate of 100 lb/ft. Value 8%  Express the total weight of the system in terms of its altitude h above the earth's surface.  Find the work done in bringing the system to an altitude of 1000 ft.

At launch, a rocket weighing 2,500,000 lbs. carries a 200,000 lb. space shuttle. Assume that in the initial stages of launch, the rocket consumes fuel at a rate of 100 lb/ft. Value 8%  Express the total weight of the system in terms of its altitude h above the earth's surface.  Find the work done in bringing the system to an altitude of 1000 ft.