View of /trunk/NationalProblemLibrary/Rochester/setIntegrals0Theory/S05.01.AreaDistance.PTP04.pg

    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 
   24 loadMacros(
   25 "PGbasicmacros.pl",
   26 "PGchoicemacros.pl",
   27 "PGanswermacros.pl",
   28 "PGauxiliaryFunctions.pl"
   29 );
   30 
   31 TEXT(beginproblem());
   32 $showPartialCorrectAnswers = 1;
   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