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{SECT 0 {PARA 3 "" 0 "" {TEXT -1 8 "Baseball" }}{PARA 0 "" 0 "" {TEXT 
-1 0 "" }}{PARA 261 "" 0 "" {TEXT -1 14 "Daniele Arcara" }}{PARA 262 "
" 0 "" {TEXT -1 25 "Department of Mathematics" }}{PARA 263 "" 0 "" 
{TEXT -1 21 "University of Georgia" }}{PARA 264 "" 0 "" {TEXT -1 18 "C
opyright (c) 2002" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{SECT 0 {PARA 4 "
" 0 "" {TEXT -1 1 " " }{TEXT 257 18 "Project:  Baseball" }}{PARA 5 "" 
0 "" {TEXT -1 13 "Your Problem:" }}{PARA 0 "" 0 "" {TEXT -1 244 "An ou
tfielder throws a ball toward home plate.  Assuming that the resistanc
e of the air is directly proportional to the speed of the ball, the po
sition of the ball (in feet) t seconds after the throw is given by fun
ctions of the following type:" }}{PARA 256 "" 0 "" {TEXT -1 7 "x(t) = \+
" }{XPPEDIT 18 0 "10*v[0]*cos(theta)*(1-exp(-1/10*t));" "6#**\"#5\"\"
\"&%\"vG6#\"\"!F%-%$cosG6#%&thetaGF%,&F%F%-%$expG6#,$*(F%F%F$!\"\"%\"t
GF%F4F4F%" }{TEXT -1 11 ",   y(t) = " }{XPPEDIT 18 0 "10*(v[0]*sin(the
ta)+320)*(1-exp(-1/10*t))-320*t+y[0];" "6#,(*(\"#5\"\"\",&*&&%\"vG6#\"
\"!F&-%$sinG6#%&thetaGF&F&\"$?$F&F&,&F&F&-%$expG6#,$*(F&F&F%!\"\"%\"tG
F&F8F8F&F&*&F1F&F9F&F8&%\"yG6#F,F&" }{TEXT -1 6 ",     " }}{PARA 0 "" 
0 "" {TEXT -1 6 "where " }{XPPEDIT 18 0 "v[0];" "6#&%\"vG6#\"\"!" }
{TEXT -1 50 " is the initial velocity (in ft/sec) of the ball, " }
{XPPEDIT 18 0 "theta;" "6#%&thetaG" }{TEXT -1 99 " is the angle that t
he trajectory of the ball forms with the ground when the ball is relea
sed, and " }{XPPEDIT 18 0 "y[0]" "6#&%\"yG6#\"\"!" }{TEXT -1 76 " is t
he initial height of the ball.  For our purposes, we shall assume that
 " }{XPPEDIT 18 0 "y[0]" "6#&%\"yG6#\"\"!" }{TEXT -1 19 " is always 7 \+
feet. " }}{SECT 0 {PARA 4 "" 0 "" {TEXT 258 21 "Part 1: An outfielder
" }}{PARA 0 "" 0 "" {TEXT -1 263 "1) An outfielder is practising.  He \+
knows that he usually throws the ball with an initial velocity of 80mp
h.  Use different angles and try to maximize his throwing distance.  I
s the best angle the same if we change the initial velocity to 85mph? \+
 How about 75mph?" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 558 "2) Assume that th
e outfielder is 300 feet away from home plate, and throws the ball wit
h an initial velocity of 80mph and the angle we found above.  How long
 does it take to the ball to reach home plate?  Where will the ball be
 in the air?  Find an angle that he could use if he wanted the catcher
 to be able to catch the ball at the plate.  Did this throw get to the
 catcher faster?  Try to find the angle that minimizes the time that t
he ball needs to reach home plate with an height between 0 and 6 feet.
  What if the initial velocity is 85mph?  Or 75mph?" }}{EXCHG {PARA 0 
"> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 0 {PARA 
4 "" 0 "" {TEXT 259 26 "Part 2: The second baseman" }}{PARA 0 "" 0 "" 
{TEXT -1 519 "The second baseman is between the outfielder and the cat
cher, and has a chance to catch the ball and throw it to home plate hi
mself.  If the ball reaches him at an height between 5 and 8 feet, it \+
takes him 1/5 of a second to catch the ball and throw it to home plate
 with an initial speed of 85mph.  See if you can find a good position \+
for the second baseman (how far should he stand from home plate?), so \+
that it would be better for the outfielder to throw him the ball rathe
r than throwing it directly to the catcher." }}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 0 {PARA 4 "" 0 "
" {TEXT 260 28 "Part 3: The third base coach" }}{PARA 0 "" 0 "" {TEXT 
-1 678 "1) A runner is on second base, and he can run home at a consta
nt speed of 25ft/sec.  You are the third baseman coach, and you have t
o decide if you send him home or not after a base hit.  The left outfi
elder catches the ball about 350ft from home plate, and he throws the \+
ball 3 seconds after the runner takes off.  You know that he usually t
hrows the ball at a speed of 85mph.  You also know that the shortstop \+
is not very good, but he is going to be 100ft from home plate to cut o
ff the ball if necessary, and throw it home at 80mph after half a seco
nd.  Do you send your runner or do you stop him at third?  (The runner
 has to run a little more than 90ft to reach home plate)" }}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}
{PARA 0 "" 0 "" {TEXT -1 120 "2) What's the slowest speed that you wou
ld need from the runner to send him home and be sure that he would rea
ch safely?" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 0 "" }}}}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 4 "" 0 "
" {TEXT -1 27 "Academic Honesty Statement:" }}{PARA 20 "" 0 "" {TEXT 
-1 208 "Place the following statement (by copying and pasting) at the \+
end of your report and sign it in ink.  Your instructor will not grade
 your report unless this signed statement appears at the end of your r
eport." }{TEXT 30 0 "" }{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" 
}}{PARA 0 "" 0 "" {TEXT -1 321 "I understand that I may work with othe
rs if I give them credit in this statement.  I also understand that I \+
am required to write my report--that to copy all or part of someone el
se's report or to allow someone else to copy all or part of my report \+
constitutes plagiarism, which is a serious violation of academic hones
ty." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 14 "I \+
worked with " }{TEXT 256 91 "(replace this parenthetical remark with f
irst and last names of those with whom you worked)" }{TEXT -1 153 " on
 this project.  I wrote my own report.  I did not copy any of this rep
ort from anyone else and I did not allow anyone else to copy any of th
is report." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 
-1 7 "Signed:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK 
"5 0" 18 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 
}