Suppose a projectile's initial velocity is specified by the initial speed \(v_{\mathrm{i}}\) and launch angle \(\theta\) instead of by its rectangular components as in Eq. 10.15

(a) Using Eqs. 10.3, write expressions for the projectile's maximum height and horizontal range in terms of \(v_{\mathrm{i}}\) and \(\theta\).

(b) What angle \(\theta\) gives the greatest value of \(y_{\max }\) ?

(c) Of \(x_{\text {max }}\) ?

x = r cos 0 y = r sin 0. (10.3)