Thursday, April 02, 2009
Bill's math and physics quiz (high school teachers: use it!; students: study for it!)
While I’m not in the classroom right now, I can still make up a mathematics quiz. High school algebra, geometry and physics teachers, have at these for making up your exams. Students, be warned.
For Question 1, assume that you are building a baseball “field of dreams” on a vacant fallow field on a farm. You lay down home plate and lay out the bases in a square, 90 feet apart as usual, and put down an outfield fence 330 feet from home plate. (We actually did this near Oberlin, Ohio in the 1950s.) Hint: you can use the Pythagorean Theorem a lot in answering these questions.
(1-1) If home plate is at the center of a circle made by the outfield fence, how far is it to dead center field for a home run?
(1-2) If the first and third base lines become chords in a circle formed by the fence, how far is it to dead center field? Is it likely that major league baseball could use this design? Why or why not?
(1-3) Starting with the situation in (1-2) how far do you have move home plate to have a distance of 400 feet to dead center? (Call this the “Oakland Coliseum effect”).
(1-4) If, instead, the first and third base lines make a perfect square with the outfield fence, with foul likes of 330 feet, how far is it to dead center field? Is this practical for baseball? (I believe that Old Shibe Park in Philadelphia and the St. Louis Browns stadium in the 1940s, where the Senators were splitting a double header on V-J day in 1945, had this design.)
(1-5) Is the pitcher’s mound (60 feet, 6 inches from home plate) in the exact middle of the diamond? Why or why not?
Question 2: Suppose you are playing a game in Fenway Park in Boston. You are playing left field. The Green Monster, the left field wall, is 37 feet high, and it is 315 feet down the left field line. The batter hits a line drive that strikes the wall on the foul line and is making an angle of 75 degrees with the wall when it hits one foot from the top of the wall. Assuming that the ball is not hooking or slicing (although it really would be) and is perfectly elastic, where do you need to be (how far from the wall) to catch the ball on the carom off the wall without it hitting the ground. Is the batter out if you succeed?
There is some Newtonian physics and some trigonometry here.
By the way, Science News has an article on “Home runs and ballparks” by Ivars Peterson, Aug. 10, 2002, here.
Question 3: Teenage Clark Kent is quarterbacking for Smallville High. From his own goal line, he throws a pass. The ball reaches a height of 50 feet. Assuming a standard 100 yard football field, how much time does Clark have to use his “powers” or “speed” to reach the other end zone in time to catch his own pass? Is this legal?
Question 4: How many ways can a team score exactly 7 points in a football game? It is impossible in American football for a team to wind up with a total of how many points?
Question 5: The nearest alien civilization with “the Grays” is on an “Earth 2” exactly 30 light years away. If you build a spaceship that can go at 99% the speed of light, and make the journey in slightly over 30 years, how much older will you be when you get there? (Okay, there is some relativity here).
Picture: RFK Stadium in Washington DC, during the Nationals's first season in 2005. It was very much a "pitcher's park" -- except for Soriano.