OUT OF LEFT FIELD
© 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)
