VectorParametric2

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Motion and Velocity with a Parametric Curve

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This PG code shows how to construct a custom answer checker that extracts the component functions from the student's answer and makes some derivative calculations with them.


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PG problem file Explanation

Problem tagging data

Problem tagging:

DOCUMENT();

loadMacros(
"PGstandard.pl",
"MathObjects.pl",
"parserVectorUtils.pl",
"AnswerFormatHelp.pl",
);

TEXT(beginproblem());

Initialization: Although not necessary for the code below, we load parserVectorUtils.pl because you may want to use some of its methods when you use this template file.

Context("Vector2D");
#Context("Vector"); # for 3d vectors
Context()->variables->are(t=>"Real");
Context()->variables->set(t=>{limits=>[0,5]});
Context()->flags->set( ijk=>0, ijkAnyDimension => 1 );

$answer = Vector("<2t,(2t)^2>");

Setup: We choose not to display the answer using ijk notation. Also, use ijkAnyDimension => 1 to require a dimension match between i,j,k vectors and either the student or the correct answer when doing vector operations.

Context()->texStrings;
BEGIN_TEXT
Find a vector parametric function \( \vec{r}(t) \) 
for a bug that moves along the parabola \( y = x^2 \) 
with velocity \( \vec{v}(t) = \langle 2, 8t \rangle \) 
for all \( t \).
$BR
$BR
\( \vec{r}(t) = \) 
\{ ans_rule(20) \}
\{ AnswerFormatHelp("vectors") \} 
END_TEXT
Context()->normalStrings;

Main Text:

$showPartialCorrectAnswers = 1;

sub mycheck {
  my ($correct, $student, $ansHash) = @_;
  my $xstu = $student . Vector(1,0);
  my $ystu = $student . Vector(0,1);
  if ( ($xstu->D('t')==Formula("2")) &&
       ($ystu->D('t')==Formula("8t")) )
  { return 1; } else { return 0; } 
}

ANS( $answer->cmp( checker=>~~&mycheck ) );

Answer Evaluation: Use dot products of the student answer with the vectors Vector(1,0) and Vector(0,1) to get the components $xstu and $ystu of the student answer. Then, we can differentiate the components just like any MathObject formula. Notice that the argument to cmp( checker => ~~&mycheck ) is our subroutine that is a custom answer checker.

Context()->texStrings;
BEGIN_SOLUTION
Solution explanation goes here.
END_SOLUTION
Context()->normalStrings;

COMMENT('MathObject version.');

ENDDOCUMENT();

Solution:

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