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# View of /trunk/NationalProblemLibrary/Rochester/instructiveProblems/OldProblems/ur_vc_12_2.pg

Fri Jul 20 19:08:31 2007 UTC (5 years, 10 months ago) by jjholt
File size: 1394 byte(s)
Added problems to sync with rochester_problib.


    1 ##DESCRIPTION
2 #
3 # File Created: 6/5/2000
5 # Problem Author: Joseph Neisendorfer
6 # WeBWorK Entry: David Etlinger
7 # Location: University of Rochester
8 #
9 # Asks for the work done when moving a
10 # particle in a vector field
11 #
12 ##ENDDESCRIPTION
13
14 ##KEYWORDS('Multivariable','Vector','Work')
15
16 DOCUMENT();        # This should be the first executable line in the problem.
17
19 "PG.pl",
20 "PGbasicmacros.pl",
21 "PGchoicemacros.pl",
23 "PGauxiliaryFunctions.pl",
24 "PGcourse.pl",
25 # source.pl"
26 );
27
28 TEXT( beginproblem() );
29 $showPartialCorrectAnswers = 1; 30 31 ################### 32 # 33 # Setup 34 35$a = random( 1, 5, 1 );
36 $b = random( 1, 5, 1 ); 37$c = random( 1, 5, 1 );
38
39 $ans = (1/2)*($a**2 + 2*$a +$b**2 + 2*$b +$c**2 + 2*$c); 40 41 ################### 42 # 43 # Text 44 45 BEGIN_TEXT 46 If C is the curve given by $$\mathbf{r} \left( t \right) = \left( 1 + a \sin t 47 \right) \mathbf{i} + \left( 1 + b \sin^{2} t \right) \mathbf{j} + \left( 1 + c 48 \sin^{3} t \right) \mathbf{k}$$, $$0 \leq t \leq \frac{\pi}{2}$$ and$BBOLD F
49 $EBOLD is the radial vector field $$\mathbf{F} \left( x, y, z \right) = x 50 \mathbf{i} + y \mathbf{j} + z \mathbf{k}$$, compute the work done by$BBOLD F
51 $EBOLD on a particle moving along C. 52$PAR
53 \{ans_rule(40)\}
54 END_TEXT
55
56 ###################
57 #