The Mathe ematics of Base eball By: Garrison Traud Jamani Perry

Transcription

1 The Mathematics of Base eball By: Garrison Traud Jamani Perry

2 Sacramento State Base eball Sacramento State baseball has been around for the past 56 years, of those years 39 have been championship hi wining i seasons. The team is currently under the guidance o head coach John Smith, who has been with the team since Coach Smith has led the team to 16 of their 39 wins, and helped bring the team up to the Division 1 rank. Sacramento State has produced 65 play yers who have moved on to the major leagues, with 8 still in the majors. 17 players from Sacramento State have been named All- background in baseball, and we can expect Americans. Sacramento State has a solid a bright future for the team this season.

3 Speed Translation Conversions: 1 meter is equivalent to feet, 1 mile is equivalent to 5280 feet. A pitcher launches a fastball at 106 miles per hour. How many feet will this ball travel in one hour, ignoring the forces of drag and gravity? How many meters is this equal to? Taking the same situation above, how far will the ball travel in half an hour? In England, a pitcher launches a ball at 1.5 meters per second. How many feet will this ball travel in 15 seconds? How many meters must this ball travel to have traveled one mile? If the farthest point from home plate is 400 feet, how long will it take the ball to reach that point, traveling in meters per second?

4 unnin To Make The Cat tch In the fifth inning of a ball game at Sac State, the pitcher, standing on the mound 26 feet from home plate, rockets a fastball to the batter. The batter smacks the ball at a 16 angle from the position the pitch crosses the plate. If the infielder runs at a 90 angle from the pitch for 25 feet, how far did the batter hit the ball? 26 Feet Pitcher 10 Feet 16 Distance of ball? 25 Feet

5 Taking It To The Gre een If you measure the length of one side of the green grass area where the pitchers mound is to be 90 feet long, what is the area of grass diamond? The perimeter? Suppose you were responsible for maintaing the field, keeping the grass healthy and all areas chalked. If fertilizer costs $14.75 per square foot, what would be the total cos to fertilize the the grass area in which the pitchers mount sits? Will $100,000 cover the costs? You need to re-chalk the base lines thatt run along the grassy area. If chalk costs $3.89 per foot, what would the total t cost be to re-chalk the base lines?

6 Defying The Odds Ignoring gravity and drag: A pitcher throws a wicked fast fastball at 100 miles per hou and the batter hits a line drive at 70% of the initial speed of the pitch, how long will it take for the ball to reach the outer extreme of the field, 400 feet? If the pitcher stands 60 (in actuality this distance is 60.6 feet) feet from home plate, how long does he have to move before the ball hits him in the face? Is it possible to have a reaction time this quick? Assuming the same scenario above, but the pitcher throwing a 50 mile per hour fastball, how long will it take the ball to reach 400 feet? How does this compare to the time when the ball was thrown at 100 milers per hour?

7 A Slice Of The Pie Assuming that the Sacramento State baseball field is exactly one fourth of a circle, a you know that the length from the extreme outfield to the pitchers mound is 400 feet what is the area of the circle? What is its circumference? What is the arc length of the portion of the circle that the baseball field covers? The diagram below depicts the above scenario, the dotted lines enclosing the baseball field. Length? 400 Feet

8 Baseballl Math In Real Life In the previous problem we explored you were asked to solve for the area and circumference of a circle given a portion of the circle, a baseball field. However, in reality that problem is not entirely accurate because the side length of the field is not equal to the length of entire field, from the pitchers mound to the 400 feet marker. Wit this in mind, how can you solve the areaa of a real life baseball field? What equations are needed to solve this irregular shape e?

9 Answer Slide Speed Translation: 559,680 feet, 170,582 meters; 279,840 feet, 85,291 meters; 73.8 feet 81 seconds. Runnin To Make The Catch: The ball only traveled feet. Taking It To The Green: Perimeter is 360 feet; Area is 8100 feet. Fertilizer cost will tota $119, 475, $100,000 will not cover the total cost. Chalk will cost $ for entire area Defying The Odds: 3.89 seconds; the pitcher has half a second to get out of the way, this guy won t make it; it will take the ball 5.45 seconds to travel 400 feet, this is not twice the time it took the ball to travel 400 feet at 100 miles per hour. A Slice Of The Pie: Circumference is 2512 feet. Area is 502,400 feet squared. Arc length is 90 feet, of one fourth of a circle.

10 Acknowledgments The Mathematics of Baseball project could not have been completed without the help of Dr. Rita Johnson, who graciously aided us in shaping and enhancing our ideas Thank you!