Serway & Jewett — Motion in Two Dimensions: Problem 16

A projectile is fired from the top of a cliff of height \(h\) above the ocean below. The projectile is fired at an angle \(\theta\) above the horizontal and with an initial speed \(v_i\). (a) Find a symbolic expression in terms of the variables \(v_i\), \(g\), and \(\theta\) for the time at which the projectile reaches its maximum height. (b) Using the result of part (a), find an expression for the maximum height \(h_{max}\) above the ocean attained by the projectile in terms of \(h\), \(v_i\), \(g\), and \(\theta\).