Chapter 10.2, Problem 81E

Projectile Motion In Exercises 81 and 82, consider a projectile launched at a height h feet above the ground and at an angle _ with the horizontal. When the initial velocity is v0 feet per second, the path of the projectile is modeled by the parametric equations

$\begin{array}{l}x=\left(v_0\cos \theta \right)t\\ \text{and}\\ y=h+\left(v_0\sin \theta \right)t-16t^2.\end{array}$

Baseball

The center field fence in a ballpark is 10 feet high and 400 feet from home plate.

The ball is hit 3 feet above the ground. It leaves the bat at an angle of $\theta$ degrees with the horizontal at a speed of 100 miles per hour.

(a) Write a set of parametric equations for the path of the ball

(b) Use a graphing utility to graph the path of the ball when $\theta ={15}^{{}^{\circ }}$. Is the hit a home run?

(c) Use a graphing utility to graph the path of the ball when $\theta ={23}^{{}^{\circ }}$. Is the hit a home run?

(d) Find the minimum angle at which the ball must leave the bat in order for the hit to be a home run.