
Consider the simple case of a ball thrown straight up starting at a position y = 0 with an initial upward velocity of magnitude v_{y}(t=0) = v_{0}. Treat gravity in the flatearth approximation and ignore air resistance.
(a) Using dimensional analysis, create a “natural length” from the parameters of this problem. (What are appropriate constants to use for this task?)
(b) Find the position, y(t), and velocity, v_{y}(t), of the ball as a function of time. (Hint: One good way to do this is to start from the equation of motion, N2, and integrate.)
(c) Find the time, t_{m}, at which the ball reaches its maximum height.
(d) Make a Taylor series for the height of the ball, y(t), about t_{m}. Keep terms through the second order.
Last revision 28. Decmber, 2010.