Problem: A rock is thrown at an angle θ above the horizontal
(a) Neglecting air resistance, use Newton's second law to find the rock's position as a function of time in the horizontal and vertical Cartesian coordinates.
(b) Let r(t) denote the distance the rock is from the starting point. For what initial angles θ will r(t) increase monotonically throughout the rock's flight? (Suggestion: To avoid long square roots, write out an expression for r^2 using results from part a).