Jennifer King & Michael RuffinoRelated Rates: Distance Between Two CarsAnd remember Aggies... Please do not drink and derive.restart:with(Maplets[Tools]): with(Maplets[Elements]):
StartEngine();randomize():lightorange:="#FFB300":
lightcyan:="#DDFFFF":
brightgreen:="#00FF00":
brightyellow:="#FFFF00":
prettyred:="#FF0000":
prettypink:="#FF007F":
neworange:="#FF8000":ColorFooter:=lightcyan:
FontFooter:=Font("helvetica",10):randASTART:=rand(-4..4):
randBSTART:=rand(-4..4):
randASPEED:=rand(1..5):randBSPEED:=rand(1..5):
randTIME:=rand(1..5):ask:=proc()
global _ASTART, _BSTART, _ASPEED, _BSPEED, _TIME, _A, _DIS, _B, _D, _ROC, _R, CarsPlot;
_BSTART:=randBSTART();
_ASTART:=randASTART();
_ASPEED:=randASPEED();
_BSPEED:=randBSPEED();
_TIME:=randTIME();
Set(starta=_ASTART);
Set(startb=_BSTART);
Set(speeda=abs(_ASPEED));
Set(speedb=abs(_BSPEED));
Set(time=_TIME);
Set(Aans="");
Set(Bans="");
Set(Dans="");
Set(ROCans="");
_B:=_BSTART+_BSPEED*_TIME;
_A:=_ASTART+_ASPEED*_TIME;
_D:=sqrt((_A)^2+(_B)^2);
_R:=(_A*_ASPEED+_B*_BSPEED)/_D;
Set(reply="");
CarsPlot:=plot([[_A,0],[0,_B]],x=-1..25,y=-1..25,color=blue);
Set(PCars=CarsPlot);
end proc:check_BSPEED:=proc()
global _BSPEED;
local userb;
userb:=Get(Bans::realcons):
#print(userb-_B<.001*_B);
#print(evalf(abs(userb-_B)<.01*abs(_B)));
if evalf(abs(userb-_B)<.01*_B) then
Set(reply="Yes! Brilliant!!!")
else
Set(reply="Ouch. Fail.")
end if;
end proc:show_BSPEED:=proc()
global _BSPEED;
Set(Bans=_B);
Set(reply="Way to be a 2% er.")
end proc:hint_BSPEED:=proc()
Set(reply="Velocity, time, and initial position are given.")
end proc:check_ASPEED:=proc()
global _ASPEED;
local userdb;
userdb:=Get(Aans::realcons):
if evalf(abs(userdb-_A)<.001*_A) then
Set(reply="Whoop! Way to go!")
else
Set(reply="Dang it... try again.")
end if;
end proc:show_ASPEED:=proc()
global _ASPEED;
Set(Aans=_A):
Set(reply="Use that muscle between your ears.")
end proc:hint_ASPEED:=proc()
Set(reply="Velocity, time, and initial position are given.")
end proc:check_DIS:=proc()
global _DIS;
local userd;
userd:=Get(Dans::realcons):
#print(userd-_D<.001*_D);
#print(evalf(abs(userd-_D)<.01*abs(_D)));
if evalf(abs(userd-_D)<.01*_D) then
Set(reply="Wow! You're rockin my socks off!!")
else
Set(reply="Ooo Burn.. or burnt orange. Sorry.")
end if;
end proc:show_DIS:=proc()
global _DIS;
Set(Dans=_D);
Set(reply="Way to be a slacker...")
end proc:hint_DIS:=proc()
Set(reply="Remember that old Pythagoras guy??..")
end proc:check_ROC:=proc()
global _ROC;
local userf;
userf:=Get(ROCans::realcons):
#print(userf-_R<.001*_R);
#print(evalf(abs(userf-_R)<.01*abs(_R)));
if evalf(abs(userf-_R)<.01*_R) then
Set(reply="OH SNAP!!")
else
Set(reply="Sorry, but no.")
end if;
end proc:show_ROC:=proc()
global _ROC;
Set(ROCans=evalf(_R));
Set(reply="Man.. that took some effort... NOT.")
end proc:hint_ROC:=proc()
Set(reply="Differentiate the equation for Question 3.")
end proc:CARS:=Maplet(onstartup=RunWindow(MAIN),
Window[MAIN](title="Related Rates: Distance Between Cars",
[ halign=none, valign=none, inset=0, spacing=0,
[ halign=none,
Button("New Problem", Evaluate(function="ask"), background=magenta),
HorizontalGlue(),
Button("Quit",Shutdown(), background=prettypink)
],
[ halign=none, inset=0, spacing=0,
[ halign=none, valign=none, inset=0,
BoxColumn( valign=none, inset=0, spacing=0, border=true,
caption="Problem Statement",
[ halign=none,
"Two cars, A and B, are moving perpendicularly from each other. Car A starts at",
TextField[starta](width=3, editable=false, background=white),
"miles from the origin ",
HorizontalGlue()
],
[ halign=none,
"going",
TextField[speeda](width=3, editable=false, background=white),
"mph in the x direction. Car B starts at",
TextField[startb](width=3, editable=false, background=white),
"miles from the origin and goes",
TextField[speedb](width=3, editable=false, background=white),
"mph in the ",
HorizontalGlue()
],
[ halign=none,
"y direction. Find the rate that the straight line distance between the two cars is changing after",
TextField[time](width=3, editable=false, background=white),
"hours.",
HorizontalGlue()
]
),
[ halign=none, border=true,
caption="Find where Car A is along the x axis after this time.",
Label("Car A is "),
TextField[Aans](width=10, background=white),
"miles away from the origin",
HorizontalGlue(),
Button("Hint", Evaluate(function="hint_ASPEED"), background=brightyellow),
Button("Check IT!", Evaluate(function="check_ASPEED"), background=brightgreen),
Button("Show", Evaluate(function="show_ASPEED"), background=prettyred)
],
[ halign=none, border=true,
caption="Find where Car B is along the y axis after this time.",
Label("Car B is "),
TextField[Bans](width=10, background=white),
"miles away from the origin",
HorizontalGlue(),
Button("Hint", Evaluate(function="hint_BSPEED"), background=brightyellow),
Button("Check IT!", Evaluate(function="check_BSPEED"), background=brightgreen),
Button("Show", Evaluate(function="show_BSPEED"), background=prettyred)
],
[ halign=none, border=true,
caption="What is the straight line distance between the two cars at this time?",
Label("Distance ="),
TextField[Dans](width=10, background=white),
"miles long",
HorizontalGlue(),
Button("Hint", Evaluate(function="hint_DIS"), background=brightyellow),
Button("Check IT!", Evaluate(function="check_DIS"), background=brightgreen),
Button("Show", Evaluate(function="show_DIS"), background=prettyred)
],
[ halign=none, border=true,
caption="What is the rate that this distance is changing at this time? (Round to thousandths)",
Label("Rate of Change ="),
TextField[ROCans](width=10, background=white),
"miles per hour",
HorizontalGlue(),
Button("Hint", Evaluate(function="hint_ROC"), background=brightyellow),
Button("Check IT!", Evaluate(function="check_ROC"), background=brightgreen),
Button("Show", Evaluate(function="show_ROC"), background=prettyred)
]
],
[ halign=none, valign=none, border=true,
caption="Cars as Points",
[ Plotter[PCars]("", width=250, height=250)
]
]
],
[ TextField[reply](width=40)
],
[ halign=none, background=ColorFooter,
Label("Programmers: Jennifer King & Michael Ruffino", font=FontFooter),
HorizontalGlue(),
Label("Copyright: P. Yasskin 2008", font=FontFooter)
]
]
)
):Maplets[Display]( CARS );