Chapter 1.7, Problem 18ES

A soccer player kicks a ball with an initial speed to $14\text{ m/s}$ at an angle $\theta$ with the horizontal (see the accompanying figure). The ball lands $18\text{ m}$ down the field. If air resistance is neglected, then the ball will have a parabolic trajectory and the horizontal range $R$ will be given by

$R=\frac{{\upsilon }^2}{g}\sin 2\theta$

where $v$ is the initial speed of the ball and $g$ is the acceleration due to gravity. Using $g=9.8{\text{ m/s}}^2$ , approximate two values of $\theta$ , to the nearest degree, at which the ball could have been kicked. Which angle results in the shorter time of flight? Why?