The USS Enterprise was the first nuclear powered aircraft ca

The USS Enterprise was the first nuclear powered aircraft carrier, commissioned in 1961. She weighs 94, 781 tons. If the USS Enterprise has a length, L = 342m and the cross-section shown below, determine the depth it sits in the water. You may assume that w = 40.5m and H = 5m. The density of saltwater is 1, 025 kg/m^3.

Solution

Solution: Given , Mass of ship (m) = 94781 tons = 94781 X 1000 Kgs

                           Length of ship , L= 342 m ; Width of ship W= 5m

Here the ship floats in the water , hence from the principle of floatation we have,

                                                    Weight of the ship = Force of buoyancy exerted on it

                                                   i.e mass of ship X g= weight of the water dispaced by ship X g

                                                                                     = volume of immersed portion of ship X density of water X g

                                                => 94781 X 1000 X 9.81 = { (1/2 * 40.5 * 5) + 5h }342 X 1025X9.81

                                                => solving we get , h = 33.82 m

Ans. Depth it sits into water=H + h= 5 +33.82 = 38.8 m