Chapter 6.3, Problem 111AYU

Projectile Motion The horizontal distance that a projectile will travel in the air (ignoring air resistance) is given by the equation

$R\left(\theta \right)=\frac{v_0^2\sin \left(2\theta \right)}{g}$

where $v_0$ is the initial velocity of the projectile, $\theta$ is the angle of elevation, and $g$ is acceleration due to gravity ( $9.8$ meters per second squared).

a. If you can throw a baseball with an initial speed of $34.8$ meters per second, at what angle of elevation $\theta$ should you direct the throw so that the ball travels a distance of 107 meters before striking the ground?

b. Determine the maximum distance that you can throw the ball.

c. Graph $R=R\left(\theta \right)$, with $v_0=34.8$ meters per second.

d. Verify the results obtained in parts (a) and (b) using a graphing utility.