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# View of /trunk/NationalProblemLibrary/Rochester/setVecFunction3Motion/ur_vc_4_7.pg

Mon May 22 17:36:35 2006 UTC (7 years ago) by jjholt
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    1 ## DESCRIPTION
2 ## Calculus
3 ## ENDDESCRIPTION
4
5 ## KEYWORDS('vector' 'acceleration' 'multivariable' 'velocity')
6 ## Tagged by tda2d
7
8 ## DBsubject('Calculus')
9 ## DBchapter('Vector Functions')
10 ## DBsection('Motion in Space: Velocity and Acceleration')
11 ## Date('')
12 ## Author('')
13 ## Institution('Rochester')
14 ## TitleText1('')
15 ## EditionText1('')
16 ## AuthorText1('')
17 ## Section1('')
18 ## Problem1('')
19
20 DOCUMENT();        # This should be the first executable line in the problem.
21
23            "PGbasicmacros.pl",
24            "PGchoicemacros.pl",
26            "PGauxiliaryFunctions.pl");
27
28 TEXT( beginproblem() );
29 $showPartialCorrectAnswers = 1; 30 31$a = non_zero_random( -5, 5, 1 );
32 $b = non_zero_random( -5, 5, 1 ); 33$asquared = $a**2; 34 35$ans1 = "- $a * sin($a * t ) + 1";
36 $ans2 = "$a * cos( $a * t ) -$a";
37 $ans3 = "($b * t**2 ) / 2 + 1";
38 $ans4 = "cos($a * t ) + t";
39 $ans5 = "sin($a * t ) - $a * t + 1"; 40$ans6 = "( $b * t**3 ) / 6 + t + 1"; 41 42 BEGIN_TEXT 43 Given that the acceleration vector is $$\mathbf{a} \left( t \right) = \left( 44 -asquared \cos \left( a t \right) \right) \mathbf{i} + \left( -asquared \sin 45 \left( a t \right) \right) \mathbf{j} + \left( b t \right) \mathbf{k}$$, the 46 initial velocity is $$\mathbf{v} \left( 0 \right) = \mathbf{i + k}$$, 47 and the initial position vector is $$\mathbf{r} \left( 0 \right) = \mathbf{i + 48 j + k}$$, compute: 49$PAR
50 A. The velocity vector $$\mathbf{v} \left( t \right) =$$ \{ans_rule(15)\} $$51 \mathbf{i} +$$ \{ans_rule(15)\} $$\mathbf{j} +$$ \{ans_rule(15)\} $$52 \mathbf{k}$$
53  $PAR 54 B. The position vector $$\mathbf{r} \left( t \right) =$$ \{ans_rule(15)\} $$55 \mathbf{i} +$$ \{ans_rule(15)\} $$\mathbf{j} +$$ \{ans_rule(15)\} $$\mathbf{k}$$ 56$PAR
57 Note: the coefficients in your answers must be entered in the form of expressions in the variable
58 \emph{t}; e.g. ${LQ}5 cos(2t)${RQ}
59 END_TEXT
60
61 ANS(fun_cmp($ans1, vars=>"t")); 62 ANS(fun_cmp($ans2, vars=>"t"));
63 ANS(fun_cmp($ans3, vars=>"t")); 64 ANS(fun_cmp($ans4, vars=>"t"));
65 ANS(fun_cmp($ans5, vars=>"t")); 66 ANS(fun_cmp($ans6, vars=>"t"));
67
68 ENDDOCUMENT();        # This should be the last executable line in the problem.