Nathan Nguyen & Nathaniel Lum
Related Rates: An Angle on FishingMath 152, Fall 2008restart;with(Maplets[Tools]): with(Maplets[Elements]):
StartEngine();randomize():lightorange:="#FFB300":
lightcyan:="#DDFFFF":ColorFooter:=lightcyan:
FontFooter:=Font("helvetica",10):
FontSymbol:=Font("symbol",16):randRate:=rand(2..7):
randHeight:=rand(5..15):
randDist:=rand(2..12)*10:ask:=proc()
global rate, height, dist, answer1, answer2;
Set(Q1="");
Set(Q2="");
rate:=randRate();
height:=randHeight();
dist:=randDist();
answer1:=evalf(arcsin(height/dist)*180/Pi);
answer2:=evalf(180*height*rate/(dist(t)^2*sqrt(1-height^2/dist(t)^2)*Pi));
Set(TFrate=rate);
Set(TFheight=height);
Set(TFdist=dist);
end proc:check1:=proc()
global answer1;
local userAns;
userAns:=Get(Q1::realcons, corrections=true, update=true);
if abs(evalf(userAns-answer1))<1/1000
then Set(reply="Correct! Move on to the next part.");
else Set(reply="Incorrect. Try again.")
end if;
end proc:show1:=proc()
global answer1;
Set(reply="Here's the answer. Try harder next time.");
Digits:=5;
Set(Q1=evalf(round(answer1*10000)/10000));
Digits:=10;
end proc:check2:=proc()
global answer2;
local userAns;
userAns:=abs(Get(Q2::realcons, corrections=true, update=true));
if abs(evalf(userAns-answer2))<1/1000
then Set(reply="Correct! Try another question.")
else Set(reply="Incorrect. Try again.")
end if;
end proc:show2:=proc()
global answer2;
Set(reply="Here's the answer. Try harder next time.");
Digits:=5;
Set(Q2=evalf(round(answer2*10000)/10000));
Digits:=10;
end proc:Fishing:=Maplet(onstartup=RunWindow(MAIN),
Window[MAIN](title="Related Rates: An Angle on Fishing",
[ [ Button("New Problem", Evaluate(function="ask"), background=magenta),
HorizontalGlue(),
Button("Quit", Shutdown(), background=pink)
],
BoxColumn( border=true, caption="Problem Statement", valign=none, spacing=0,
[ halign=none,
"A fish is reeled in at a rate of",
TextField[TFrate](width=3, editable=false, background=white),
"ft/s from a point",
TextField[TFheight](width=3, editable=false, background=white),
"ft above the water.",
HorizontalGlue()
],
[ halign=none,
"When there are still",
TextField[TFdist](width=3, editable=false, background=white),
"ft of fishing line out, find the angle between the line and",
HorizontalGlue()
],
[ halign=none,
"the water and the rate it is decreasing. Give answers in degrees to 3 decimal places.",
HorizontalGlue()
]
),
[ border=true, halign=none,
"Find the angle between the line and the water:.",
HorizontalGlue(),
Label("q =", font=FontSymbol),
TextField[Q1](width=6, background=white),
Button("Check", Evaluate(function="check1"), background=green),
Button("Show", Evaluate(function="show1"), background=lightorange)
],
[ border=true, halign=none,
"Find the rate at which the angle is decreasing:",
HorizontalGlue(),
Label("q", font=FontSymbol), "' =",
TextField[Q2](width=6, background=white),
Button("Check", Evaluate(function="check2"), background=green),
Button("Show", Evaluate(function="show2"), background=lightorange)
],
[
TextField[reply](width=60, editable=false, background=white)
],
[ halign=none, background=ColorFooter,
Label("Programmers: Nathan Nguyen & Nathaniel Lum", font=FontFooter),
HorizontalGlue(),
Label("Copyright: P. Yasskin 2008", font=FontFooter)
]
]
)):Maplets[Display](Fishing);