ver m( t ) = up USEFUL INFORMATION COM? solve E Chain rule: - du = dt L = Iw , where I is the moment of inertia of a rigid object and w its angular velocity Isphere = = Mr2, Vsphere = 3 r is the radius of the sphere, M is the mass of the solid sphere. Mass density p = Change in momentum for a rocket with exhaust velocity Vex is dP = mdu + Vexdm Cartesian coordinates dV = dxdydz Cylindrical coordinates dV = rdrdqdz Spherical coordinates dV = r2 sin 0 drd0dy, z = r cos 0 sin 20 = 2 sin 0 cos 0 1 - cos 20 sin20 = Trigonometry 2 1 + cos 20 cos2 0 = 2 dx Integrals = Inx XProblem 2 (35 points) Consider a rocket taking off from rest and traveling in a straight line upward in a downward pointing vertical moty gravitational field g. The initial mass of the rocket at t = 0 is mo and the mass at any given time is m(t) = mo - kt. Ignore air drag. A. Write the equation of motion for the rocket (use information on front page). (17 points) Use off = - mg B. Use the chain rule (see front page) to solve the equation of motion for the speed of the rocket as a function of position. (18 points)