1. The problem statement, all variables and given/known data Postal workers on planet Vashtup want to drill a straight tube through the planet, starting at Post Oﬃce 1, passing through the center of the planet, and ending on the other side at Post Oﬃce 2. They plan to release small packages containing mail into the tube from P.O. 1 and have others grab them at P.O. 2. Vashtup has g = 9.1 m/s2 , and a radius of 5200 km. When it is located within the shell of a planet, the weight of a particle of mass m is mgr/R, where r is its distance from the center of the planet. Assume that there is no air resistance. Compute a) the position r of the package 1088 s after it has been released, and b) its speed at that time. Note: r is positive if the package is on the same side of planet as P.O. 1, and negative if it is on the same side as P.O. 2. 2. Relevant equations F=ma 3. The attempt at a solution Note: My professor wants me to be using differential equations to solve this. I think I have a basic idea of how to do this problem, but am having trouble finding an equation that correctly models the motion of the object dropped into the tube. From what is given I have: ma=mgr/R a=gr/R a is the second derivative of position, so x''=gr/R Now, this is where I'm having trouble. I know I need to find r(t), or a function for position dependent on time but I'm not seeing how to make that connection. I tried using the above equation saying (R/g) r''(t) = r(t), y'(0)=0, y(0)=R but that definitely isn't right Any ideas?