View of /trunk/NationalProblemLibrary/ASU-topics/setCalculus/stef/stef13_4p2.pg

    1 ## DESCRIPTION
    2 ## Calculus
    3 ## ENDDESCRIPTION
    4 
    5 ## KEYWORDS('vectors', 'acceleration')
    6 ## Tagged by YL
    7 
    8 ## DBsubject('Calculus')
    9 ## DBchapter('Vector Functions')
   10 ## DBsection('Derivatives and Integrals of Vector Functions')
   11 ## Date('')
   12 ## Author('')
   13 ## Institution('ASU')
   14 ## TitleText1('Calculus: Early Transcendentals')
   15 ## EditionText1('5')
   16 ## AuthorText1('Stewart')
   17 ## Section1('13.2')
   18 ## Problem1('')
   19 
   20 ## TitleText2('Calculus: Early Transcendentals')
   21 ## EditionText2('6')
   22 ## AuthorText2('Stewart')
   23 ## Section2('13.2')
   24 ## Problem2('')
   25 
   26 DOCUMENT();        # This should be the first executable line in the problem.
   27 
   28 loadMacros("PG.pl",
   29            "PGbasicmacros.pl",
   30            "PGchoicemacros.pl",
   31            "PGanswermacros.pl",
   32            "PGauxiliaryFunctions.pl");
   33 
   34 TEXT( beginproblem() );
   35 $showPartialCorrectAnswers = 1;
   36 
   37 $a = non_zero_random( -8, 8, 1 );
   38 $b = non_zero_random( -8, 8, 1 );
   39 
   40 
   41 BEGIN_TEXT
   42 
   43 If \( \mathbf{r} (t) = \cos ($b t) \mathbf{i} + \sin ($b t) \mathbf{j} + $a t \mathbf{k} \),
   44 compute the tangential and normal components of the acceleration vector.
   45   $PAR
   46  Tangential component  \(\; a_T (t) = \) \{ans_rule(15)\}
   47 $PAR
   48  Normal component \(\; a_N (t) = \) \{ans_rule(15)\}
   49 
   50 END_TEXT
   51 
   52 ANS(fun_cmp(0, vars=>"t"));
   53 ANS(fun_cmp($b**2, vars=>"t"));
   54 
   55 ENDDOCUMENT();        # This should be the last executable line in the problem.