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

question 95

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) \(11.3 ^ { \circ }\)

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