Problem 2.2 Rocket departing from Earth Consider a rocket that takes off from earth. It accelerates by burning fuel. Assume that the rocket hurls out fuel at a constant rate, as in the example discussed in the lecture. At the same time, it is subject to gravity. Find the equation of motion and solve it when the rocket is close to the surface, such that you can assume that the gravitational eld is homogeneous. Assume that the velocity vanishes at t = 0. Problem 2.3 Center of mass of a paraboloid A paraboloid emerges by rotating a parabola about its symmetry axis, see Figure 2.22. Con- sider the homogeneous paraboloid consisting of (x, y, z) E R3 satisfying x2+y2saz for 0 S z S b with 51,!) > 0. Determine its volume. Use symmetry arguments to con x clude that the center of mass lies on the zaxis. . Figure 2.22: Paraboloid. Compute the location of the center of mass