1. The problem statement, all variables and given/known data A body of mass m is taken at a constant speed from the surface of the earth (radius = Re) to infinity. (a) What is the work W1 done on the body in the process? (b) If m is taken from a distance r > Re to infinity, how much work W2 is required? (c)Which quantity is larger, W1 or W2? Why? (d) How much work is required to take the body from Re to r? (e) The body is dropped from r with no initial velocity. Find an expression for the velocity with which it hits the earth's surface. (Neglect all frictional forces) (f) With what minimum velocity must m be thrown upward in order to reach an altitude h = r-Re (g) If m is thrown with the above velocity upward but not exactly vertically, will it reach the above altitude? Explain your answer. (h) What is the potential energy U of the body at altitude h? (i) What is the potential energy U of the body at the surface of the earth? (j) Which is more, the potential energy at the surface or that at altitude h?How much more? (k) Is the work done on m taking it from the surface to altitude h equal to the increase in potential energy of m? 2. Relevant equations U(r) = -GMm/r 3. The attempt at a solution For a) I did an integral from Re to infinity and got W1=GMm/R For b) I did the same from r to infinity and got W2= GMm/r For c) I took did GMm/r - GMm/Re = GMm (1/r - 1/Re) so W1>W2 For d) I took the integral from Re to r and got GMm ( -1/r + 1/Re) I'm not sure of (e) onwards For e) I have an idea that K.E = P.E so 1/2 (mv^2) = U but I'm not sure what U in this case will be. I know it can't be negative.