In calculus, a model for projectile motion with no friction is considered, and a "parabolic trajectory" is obtained. If the initial velocity is and is the initial angle to the horizontal, then the parametric equations for the horizontal and vertical components of the position vector are (1) , and (2) . Solve equation (1) for t and get , then replace this value of t in equation (2) and the result is , which is an equation of a parabola. The time required to reach the maximum height is found by solving : , yields , and the maximum height is . The time till impact is found by solving , which yields , and for this model, . The range is found by calculating : . For a fixed initial velocity , the range is a function of , and is maximum when . Numerical solution of second order D. E.'s This module illustrates numerical solutions of a second order differential equatio