Meriam, Kraige & Bolton — Kinematics of Particles: Problem 2_35

2/35 When the effect of aerodynamic drag is included, the y-acceleration of a baseball moving vertically upward is \(a_u = -g - kv^2\), while the acceleration when the ball is moving downward is \(a_d = -g + kv^2\), where \(k\) is a positive constant and \(v\) is the speed in meters per second. If the ball is thrown upward at 30 m/s from essentially ground level, compute its maximum height \(h\) and its speed \(v_f\) upon impact with the ground. Take \(k\) to be \(0.006 \text{ m}^{-1}\) and assume that \(g\) is constant.