© Mathalicious 2014 OUT OF LEFT FIELD name date In which MLB ballpark is it hardest to hit a home run? Act One: Going Yard 1 The left field wall in Boston’s Fenway Park – aka Green Monster – is 315 feet from home plate and 37 feet tall. The following equations represent three hypothetical trajectories of a baseball hit down the left field line. For each, determine the maximum height the ball would reach, how far it would travel (assuming it landed on the ground), and whether it would be a home run. Then, draw a rough sketch of the ball’s flight path. Height y = -­‐0.0002(d – 182)2 + 10 y = -­‐0.004(d – 173)2 + 123 y = -­‐0.08(d – 49)2 + 195 Max. Height Distance Home Run? Height (feet) 200 175 150 125 100 75 50 25 0 0 30 60 90 120 150 180 210 240 270 300 330 360 390 420 Distance from Home Plate (feet) 2 The table below shows the height of and distance to the left field (LF) wall in six other major league ballparks. Would the home run(s) above have cleared the left field wall in each of these parks, too? Team Yankees Rockies Rangers Cubs Rays Cardinals Distance, LF 318 feet 347 feet 334 feet 355 feet 315 feet 336 feet 8 feet 8 feet 14 feet 16 feet 9.5 feet 9 feet Height, LF 2 Act Two: Ballpark Tour 3 During the 2013 Major League Baseball season, a home run over the left field wall typically reached a maximum height of 81 feet, and [would have] traveled a distance of 378 feet from home plate. Assuming the average batter hits the ball three feet from the ground, write a function for the trajectory of the average home run. 4 The table below shows the distance to and height of every left field wall in the major leagues. Would the average home run clear every wall? Also, which ballpark is the easiest for home runs, and which is the hardest? Explain. Team Distance Height Orioles 333 ft 7 ft Red Sox 315 ft White Sox Team Distance Height Athletics 330 ft 8 ft 37 ft Mariners 331 ft 330 ft 8 ft Rays Indians 325 ft 19 ft Tigers 345 ft Astros Team Distance Height Dodgers 330 ft 3.83 ft 8 ft Marlins 330 ft 8 ft 315 ft 9.5 ft Brewers 344 ft 10 ft Rangers 334 ft 14 ft Mets 335 ft 12 ft 8 ft Blue Jays 328 ft 10 ft Phillies 329 ft 9.25 ft 315 ft 21 ft D’Backs 330 ft 7.5 ft Pirates 325 ft 6 ft Royals 330 ft 9 ft Braves 335 ft 8 ft Padres 334 ft 4 ft Angels 330 ft 4.75 ft Cubs 355 ft 16 ft Giants 339 ft 8 ft Twins 339 ft 8 ft Reds 328 ft 12 ft Cardinals 336 ft 9 ft Yankees 318 ft 8 ft Rockies 347 ft 8 ft Nationals 336 ft 8 ft 5 The graphs show the average trajectories for left field home runs in Denver, CO (Rockies), St. Petersburg, FL Height (feet) (Rays), and Philadelphia, PA (Phillies). As you can see, they’re not actually parabolas. Why do you think this is? 100 75 50 25 0 0 70 140 210 280 350 420 Distance from Home Plate (feet)