Question

Jacob's Field In Jacob's Field, the home of the Cleveland Indians, the distance from home plate to the outfield fence varies from 325 feet (1" and 3" base lines) to 410 feet (straightaway center field). We wish to estimate the minimum distance from home plate to the highest point of Jacob's Field and from the base of the outfield fence to the highest point of the stadium so we can estimate the minimum distance that a ball must travel to be hit out of Jacob's Field. We begin by sketching a picture showing home plate, the fence, and the highest point of the stadium. Draw lines from home plate to the base of the fence and from the base of the fence to the highest point. Using a device to measure angles of elevation, the angle of elevation from home plate to the highest point of the stadium in straightaway center field is 10°. The angle of elevation from the base of the fence to the highest point of the stadium is 32.5°. d = minimal distance 10° = a 410' =L 32.5° =B 1.) Using this information, determine the value for d, which is the minimum distance that a ball must travel from home plate to the highest point in the stadium. 2.) Develop a general formula for computing d, the distance from home plate to the highest point of the stadium. Leta and B denote the angles of elevation to the top of the roof from home plate and the base of the outfield wall, respectively. Let L be the distance from home plate to the outfield fence. 3.) Write your final formula from part 2 in the form Distance Lsin B sin(-a) Be sure to show all intermediate steps.

Answer 1

PAGE NO DATE: 1 201 ) К. с- . 44 он В = 325 а) P W/R tan ßa (r = y Cats tan da рь Еу +L ?л ? Я сод 32-5 + 416 41 о+7(* - Sъ96) (б. 1263) = 8 410 + (0-26+) = 8 Го: +7 32 ) = y = Г6, 92 41. б К= (а+ В Бу 6-92 х (1 569) 809 - 83 р- lth a 41o + 389 .83 129 9 Ф 2

PAGE HO DATE 1201 2 DE (1299.83)*+ 2+(566-9222 2 2609550.0209 + 32 1398.2864 2010 95 63153 :3153 2418108 feet D B K tan ß= Tu y Catß fond 9/Ltr (1+x) y Cata (L+K-M) y (at pa- carp) y (cath- coop) by figure Sind yo عه D. sind D. sind (catha Coff) t sindfath- cosp)

PAGE No DATE 201 B Da Sind Crotta Catß) D Sina . Cosp Cold sind sina (cata - capp) Son) D (cosa dirß cos.p.sina) finde sin ß L sina Sin ipd)) = L sinß 2013 I Sinß y'n (f-d) proved