Consider a projectile launched at a height h feet abovethe ground and at an angle ? with the horizontal. If theinitial velocity is v0 feet per second, thepath of the projectile is modeled by the parametric equations
x =t(v0cos(?))
and
y = h +(v0sin(?))t ?16t2.
The center field fence in a ballpark is 10 feet high and 400 feetfrom home plate. The ball is hit h = 3 feet above theground. It leaves the bat at an angle of ? degrees withthe horizontal at a speed of 107 miles per hour (see figure).
(a) Write a set of parametric equations for the path of theball. (Write your equations in terms of t and?.)
(b) Use a graphing utility to graph the path of the ball when? = 15°. Is the hit a home run?
YesNo
(c) Use a graphing utility to graph the path of the ball when? = 23°. Is the hit a home run?
YesNo
(d) Find the minimum angle at which the ball must leave the bat inorder for the hit to be a home run. (Round your answer to onedecimal place.)
°
