John Kirgis & Travis KocianRelated Rates: Boat Being Pulled Into a Dockrestart:with(Maplets[Tools]): with(Maplets[Elements]): with(plots):# with(plottools):
StartEngine();randomize():lightorange:="#FFB300":
lightcyan:="#DDFFFF":
lightblue:="#AAAAFF":ColorFooter:=lightcyan:
FontFooter:=Font("helvetica",10):randdc:=rand(1..5):
randa:=rand(6..12):
randc:=rand(1..5):ask:=proc()
global c, dc, a, b, db, K, f, Aniboat;
a:=randa();
c:=a+randc();
dc:=randdc();
b:=sqrt(c^2-a^2);
db:=c*dc/b;
Set(TFdc=dc);
Set(TFc=c);
Set(TFa=a);
Set(TFform_1=" ");
Set(TFform_2=" ");
Set(TFb=" ");
Set(TFdb=" ");
Set(reply=" ");
K:=a/A:
f:=x->-K*x+a:
Set(Pboat(play)=false);
Aniboat:=animate(plot, [f(x), x=0..b+5, y=0..a+3], A=b+3..b-3);
Set(Pboat=Aniboat);
end proc:hint_1:=proc()
Set(reply=" Use the Pythagorean Theorum.")
end proc:check_1:=proc()
global b;
local userform_1;
userform_1:=Get(TFform_1):
if userform_1="(c^2-a^2)^(1/2)" then
Set(reply="Neato!")
else
Set(reply="Oh, too bad. Try again.")
end if;
end proc:show_1:=proc()
global b;
Set(TFform_1=('c'^2-'a'^2)^(1/2));
Set(reply=" Try for yourself next time.")
end proc:hint_2:=proc()
Set(reply=" Just plug the numbers into your equation. Make sure you type it in right.")
end proc:check_2:=proc()
global b;
local userb;
userb:=Get(TFb::realcons):
if userb=b then
Set(reply="Someone deserves a cookie!")
else
Set(reply="Oh, too bad. Try again.")
end if;
end proc:show_2:=proc()
global b;
Set(TFb=b);
Set(reply=" Try for yourself next time.")
end proc:hint_3:=proc()
Set(reply=" Use the implicit method to get the derivative of the Pythagorean Theorum.")
end proc:check_3:=proc()
global db;
local userform_2;
userform_2:=Get(TFform_2):
if userform_2="c/b*dc/dt" then
Set(reply="Fantastic!")
else
Set(reply="Oh, too bad. Try again.")
end if;
end proc:show_3:=proc()
global db;
Set(TFform_2="c/b*dc/dt");
Set(reply=" Try for yourself next time.")
end proc:hint_4:=proc()
Set(reply=" Just plug the numbers into your equation. Be sure to type it in right.")
end proc:check_4:=proc()
global db;
local userdb;
userdb:=Get(TFdb::realcons):
if userdb=value(db) then
Set(reply="I'd give you a high five, but I don't have fingers.")
else
Set(reply="Oh, too bad. Try again.")
end if;
end proc:show_4:=proc()
global db;
Set(TFdb=db);
Set(reply=" Try for yourself next time.")
end proc:BoatDocking:=Maplet(onstartup=RunWindow(MAIN),
Window[MAIN](title="Boat Being Pulled Into a Dock",
[ halign=none, valign=none, inset=0,
[ halign=none,
Button("New Problem", Evaluate(function="ask"), background=magenta),
HorizontalGlue(),
Button("Quit",Shutdown(), background=pink)
],
[ [ valign=none, inset=0, spacing=0, border=true,
caption="Problem Statement",
[ halign=none,
"A boat is being pulled into a dock by a rope connected to a winch on the edge of the dock.",
HorizontalGlue()
],
[ "The rope is being pulled in at a constant rate of ",
TextField[TFdc](width=3, editable=false, background=white),
"ft/sec.",
HorizontalGlue()
],
[ "and the height of the dock is",
TextField[TFa](width=3, editable=false, background=white),
"ft. above the water level.",
HorizontalGlue()
],
[ "Determine the velocity of the boat when the length of the rope between the boat and the winch is ",
TextField[TFc](width=3, editable=false, background=white),
"ft.",
HorizontalGlue()
]
],
[ halign=none, valign=none, border=true,
caption="Animation",
[ Button[BPlay]("Play",
onclick=SetOption(Pboat(play)=true), background=lightblue),
Button[BStop]("Stop",
onclick=SetOption(Pboat(pause)=true), background=lightblue),
Button[BForward]("Forward",
onclick=Action(SetOption(Pboat(pause)=true),
SetOption(Pboat(frame_forward)=true)), background=lightblue),
Button[BReverse]("Reverse",
onclick=Action(SetOption(Pboat(pause)=true),
SetOption(Pboat(frame_backwards)=true)), background=lightblue)
],
[ Plotter[Pboat]("", width=250, height=250)
]
]
],
[ halign=none, inset=0, spacing=0,
[ halign=none, valign=none, inset=0,
[ halign=none, border=true,
caption="Write the formula for the distance between the boat and the base of the dock.",
"b = ",
TextField[TFform_1](width=15, background=cyan),
HorizontalGlue(),
Button("Hint", Evaluate(function="hint_1"), background=yellow),
Button("Check", Evaluate(function="check_1"), background=green),
Button("Show", Evaluate(function="show_1"), background=lightorange)
],
[ halign=none, border=true,
caption="Solve your formula for the distance between the boat and the base of the dock.",
"b = ",
TextField[TFb](width=15, background=cyan),
HorizontalGlue(),
Button("Hint", Evaluate(function="hint_2"), background=yellow),
Button("Check", Evaluate(function="check_2"), background=green),
Button("Show", Evaluate(function="show_2"), background=lightorange)
]
],
[ halign=none, valign=none, inset=0,
[ halign=none, border=true,
caption="Write the formula for the velocity of the boat under the given conditions.",
"db/dt = ",
TextField[TFform_2](width=15, background=cyan),
HorizontalGlue(),
Button("Hint", Evaluate(function="hint_3"), background=yellow),
Button("Check", Evaluate(function="check_3"), background=green),
Button("Show", Evaluate(function="show_3"), background=lightorange)
],
[ halign=none, border=true,
caption="Solve your formula for the distance between the boat and the base of the dock.",
"db/dt = ",
TextField[TFdb](width=15, background=cyan),
HorizontalGlue(),
Button("Hint", Evaluate(function="hint_4"), background=yellow),
Button("Check", Evaluate(function="check_4"), background=green),
Button("Show", Evaluate(function="show_4"), background=lightorange)
]
]
],
TextField[reply](width=40),
[ halign=none, background=ColorFooter,
Label("Programmers: John Kirgis & Travis Kocian", font=FontFooter),
HorizontalGlue(),
Label("Copyright: P. Yasskin 2008", font=FontFooter)
]
])):Maplets[Display](BoatDocking);