A ball is projected vertically upward from the top of a 25-m high cliff with an initial velocity of 14 m/s. Assume the only force acting after launch is gravity, producing a constant downward acceleration of 9.8 m/s2. Motion takes place along a vertical axis with upward positive.
(a) Express the acceleration a(t) of the ball as a constant second derivative of its height s(t) measured from the ground.
(b) Integrate to obtain the velocity function v(t), and determine the time at which the ball reaches its highest point.
(c) Find the height of the ball above the ground at the instant identified in part (b).
(d) Calculate the total time elapsed from launch until the ball first hits the ground at the base of the cliff.