While we usually assume that the force of gravity is constant, it actually decreases with altitude according to the formula Fgrav = mgr^2_o / r^2, where ro is the radius of Earth, and r is the distance from the Earth's center.
a) Why can we approximate the force of gravity as constant at the surface of Earth?
b) Show that a(r)dr = vdv.
c) If the particle is fired vertically with velocity vo from Earth's surface, determine its velocity as a function of position r. (Hint: use the result of part b)