Space Capsule Design You are part of a team of engineers designing the Apollo space-capsule. The capsule is composed of two parts: A cone with a...

can someone really help me? Thank you

It is really hard, since physics and calculus are involved

Space Capsule DesignYou are part of a team of engineers designing the Apollo space-capsule. The capsuleis composed of two parts:1. A cone with a height of 4 meters and a base of radius 3 meters;2. A re-entry shield in the shape of a parabola revolved about the axis of the cone,which is attached to the cone along the edge of the base of the cone. Its vertex isa distance D below the base of the cone.Assume the capsule has uniform density p. Your project director has specified thatthe center of mass of the capsule should be below the center of mass of the displacedwater because he believes this will give the capsule better stability in heavy seas. Hehas given your team the task of finding values of the design parameters D and p so thatthe capsule will float with the vertex of the cone pointing up and with the waterline 2meters below the top of the cone, in order to keep the exit port | meter above water.a. Show your project director that this task is impossible; i.e., there are no values ofD and p that satisfy the design specifications.b. Prove that you can solve this dilemma by incorporating a flotation collar in theshape of a torus (doughnut). The collar will be made by taking hollow plastictubing with a circular cross section of radius 1 meter and wrapping it in a circularring about the capsule, so that it fits snugly. The collar is designed to float justsubmerged with its top tangent to the surface of the water. Show that this flotationcollar makes the capsule plus collar assembly satisfy the design specifications. Findthe density p needed to make the capsule float at the 2 meter mark. Assume theweight of the tubing is negligible compared to the weight of the capsule, that thedesign parameter D is equal to 1 meter, and the density of water is 1.Your investigations will be guided by a physical principle (1), a formula, whichyou will derive (II), and a theorem which you will state and prove (III).L. Archimedes' Principle: A body floats in a fluid at the level at which the weight ofthe displaced fluid equals the weight of the body.II. Consider the region bounded by the graph of a = f(y), the y-axis, and the linesy = e and y = d. Derive a formula for the center of mass of the solid formed byrevolving this region about the y-axis. Explain why the center of mass is on they-axis so you just have to find y.