The Parametric Equations for the Path of a Projectile Launched $\theta$

Multiple Choice

The parametric equations for the path of a projectile launched at a height h feet above the ground, at an angle $\theta$ with the horizontal and having an initial velocity of $v _ { 0 }$ feet per second is given by $x = \left( v _ { 0 } \cos \theta \right) t$ and $y = h + \left( v _ { 0 } \sin \theta \right) t - 16 t ^ { 2 }$ . 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 as shown in the figure. Find the minimum angle at which the ball must leave the bat in order for the hit to be a home run using the parametric equations $x = \left( \frac { 440 } { 3 } \cos \theta \right) t$ and $y = 3 + \left( \frac { 440 } { 3 } \sin \theta \right) t - 16 t ^ { 2 }$ . Round your answer to one decimal place.

A) $25.5 ^ { \circ }$
B) $19.4 ^ { \circ }$
C) $3.4 ^ { \circ }$
D) $4.5 ^ { \circ }$
E) $11.3 ^ { \circ }$