[npl] / trunk / NationalProblemLibrary / Rochester / setIntegrals0Theory / S05.01.AreaDistance.PTP04.pg Repository: Repository Listing bbplugincoursesdistsnplrochestersystemwww

Thu Aug 7 13:44:57 2008 UTC (4 years, 9 months ago) by gage
File size: 1727 byte(s)
``` Adding in questions written by Paul Pearson
```

```    1 ##DESCRIPTION
2 ##KEYWORDS('derivatives', 'antiderivatives', 'distance,velocity,acceleration')
3 ##  Given initial velocity, and position of the stone thrown up, figure
4 ##  out its position after a seconds, time when it hits the ground and
5 ##  velocity with which it hits the ground
6 ##ENDDESCRIPTION
7
8 ## DBsubject('Calculus')
9 ## DBchapter('Integrals')
10 ## DBsection('Area and Distance')
11 ## Date('6/3/2008')
12 ## Author('Paul Pearson')
13 ## Institution('University of Rochester')
14 ## TitleText1('Calculus: Early Transcendentals')
15 ## EditionText1('6')
16 ## AuthorText1('Stewart')
17 ## Section1('5.1')
18 ## Problem1('3')
19
20 ## Original:  /rochesterLibrary/setDerivatives20Antideriv/s3_10_56.pg
21
22 DOCUMENT();
23
25 "PGbasicmacros.pl",
26 "PGchoicemacros.pl",
28 "PGauxiliaryFunctions.pl"
29 );
30
31 TEXT(beginproblem());
33
34 \$s1 = random(600,1000,25);
35 \$v1 = random(10,20,2);
36 \$t1 = random(2,6,1);
37
38 TEXT(EV2(<<EOT));
39 A stone is thrown straight up from the edge of a roof,
40  \$s1   feet above the ground, at a speed of \$v1
41 feet per second.  \$BR
42 A.  Remembering that the acceleration due to gravity
43 is  -32  feet per second squared, how high is the stone \$t1
44 seconds later?  \{ans_rule(30) \}. \$BR
45 Don't forget to enter the correct \{ helpLink('units') \}.
46 \$BR
47 EOT
48
49 \$ans =  -16*\$t1**2 + \$v1*\$t1 + \$s1;
50 ANS(num_cmp("\$ans", units => 'ft'));
51
52 TEXT(EV2(<<EOT));
53 B.  At what time does the stone hit the ground? \{ans_rule(30) \}. \$BR
54 EOT
55 \$t2 = (\$v1 + sqrt( \$v1*\$v1+64*\$s1))/32;
56 \$ans =  \$t2;
57 ANS(num_cmp("\$ans", units => 's'));
58
59 TEXT(EV2(<<EOT));
60 C.  What is the velocity of the stone when it
61 hits the ground? \{ans_rule(30) \}.
62 EOT
63
64 \$ans =  -32*\$t2 + \$v1;
65 ANS(num_cmp("\$ans", units => 'ft/s' ));
66
67 ENDDOCUMENT();
68
```