Related Rates: Ladder
John Horn
restart:
with(Maplets[Tools]): with(Maplets[Elements]): with(plots): with(plottools):
StartEngine();
randomize():
lightorange:="#FFB300":
randL:=rand(1..3):
randa:=rand(1..15):
randda:=rand(1..5):
ask:=proc()
global _L, __a, _da, __b, _db, pa, pb, y1, LadderAnimate;
__a:=randa();
_L:=__a+randL();
_da:=-randda();
Set(TFL=_L);
Set(TFa=__a);
Set(TFda=abs(_da));
Set(TFb="");
Set(TFdb="");
__b:=sqrt(_L^2-__a^2);
_db:=-__a/__b*_da;
Set(reply="");
pb:=sqrt(_L^2-a^2);
y1:=-a/pb*b+a;
Set(PLadder(play)=false);
LadderAnimate:=animate(plot, [y1, b=0..pb,0.._L, labels=["b","a"]], a=__a-.001..0, view=[0.._L,0.._L], tickmarks=[[_L],[__a,_L]]);
Set(PLadder=LadderAnimate);
end proc:
check_b:=proc()
global __b;
local userb;
userb:=Get(TFb::realcons):
#print(userb-__b<.001*__b);
#print(evalf(abs(userb-__b)<.01*abs(__b)));
if evalf(abs(userb-__b)<.01*__b) then
Set(reply="Correct!")
else
Set(reply="Incorrect. Try again.")
end if;
end proc:
show_b:=proc()
global __b;
Set(TFb=__b);
Set(reply="")
end proc:
hint_b:=proc()
Set(reply=" Use the Pythagorean Theorem.")
end proc:
check_db:=proc()
global _db;
local userdb;
userdb:=Get(TFdb::realcons):
if evalf(abs(userdb-_db)<.001*_db) then
Set(reply="Correct!")
else
Set(reply="Incorrect. Try again.")
end if;
end proc:
show_db:=proc()
global _db;
Set(TFdb=_db):
Set(reply="")
end proc:
hint_db:=proc()
Set(reply=" Implicitly differentiate your Pythagorean Theorem equation. The ladder length is constant.")
end proc:
Ladder:=Maplet(onstartup=RunWindow(MAIN),
Font[helv10]("helvetica",10),
Window[MAIN](title="Ladder Sliding down a Wall",
[ halign=none, valign=none, inset=0, spacing=0,
[ halign=none,
Button("New Problem", Evaluate(function="ask"), background=magenta),
HorizontalGlue(),
Button("Quit",Shutdown(), background=pink)
],
[ 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,
"If a ladder of Length",
TextField[TFL](width=3, editable=false, background=white),
"ft is falling down a wall at a rate of",
TextField[TFda](width=3, editable=false, background=white),
"ft/min,",
HorizontalGlue()
],
[ halign=none,
"what is the distance of the ladder base to the wall and the rate of change",
HorizontalGlue()
],
[ halign=none,
"of this distance when the ladder is at height",
TextField[TFa](width=3, editable=false, background=white),
"ft. on the wall?",
HorizontalGlue()
]
),
VerticalGlue(),
[ halign=none, border=true,
caption="Find the distance from the base to the wall:",
Label("b = "), TextField[TFb](width=10, background=turquoise),
HorizontalGlue(),
Button("Hint", Evaluate(function="hint_b"), background=lightorange),
Button("Check", Evaluate(function="check_b"), background=green),
Button("Show", Evaluate(function="show_b"), background=lightorange)
],
VerticalGlue(),
[ halign=none, border=true,
caption="Find the rate of change of this distance:",
Label("db/dt ="), TextField[TFdb](width=10, background=turquoise),
HorizontalGlue(),
Button("Hint", Evaluate(function="hint_db"), background=lightorange),
Button("Check", Evaluate(function="check_db"), background=green),
Button("Show", Evaluate(function="show_db"), background=lightorange)
]
],
[ halign=none, valign=none, border=true,
caption="Animation",
[ Button[BPlay]("Play", onclick=SetOption(PLadder(play)=true), background=tan),
Button[BStop]("Stop", onclick=SetOption(PLadder(pause)=true), background=tan),
Button[BForward]("Forward", onclick=Action(SetOption(PLadder(pause)=true),
SetOption(PLadder(frame_forward)=true)), background=tan),
Button[BReverse]("Reverse", onclick=Action(SetOption(PLadder(pause)=true),
SetOption(PLadder(frame_backwards)=true)), background=tan)
],
[ Plotter[PLadder]("", width=250, height=250)
]
]
],
[ TextField[reply](width=40)
],
[ background="#DDFFFF", inset=0, spacing=0,
Label("Programmer: John Horn", font=helv10),
HorizontalGlue(),
Label("@ Copyright P. Yasskin 2007", font=helv10)
]
]
)
):
Maplets[Display]( Ladder );