View of /trunk/NationalProblemLibrary/Rochester/setLimitsRates1TangentVelocity/s1_1_5.pg

    1 ##DESCRIPTION
    2 ##  Find the velocity of a ball thrown straight up during periods of time
    3 ##  approaching a value, then guess the instantaneous velocity at that point
    4 ##ENDDESCRIPTION
    5 
    6 ##KEYWORDS('Calculus')
    7 ##Tagged by ynw2d
    8 
    9 ##DBsubject('Calculus')
   10 ##DBchapter('Limits and Derivatives')
   11 ## DBsection('Tangents, Velocities, and Other Rates of Change')
   12 ## TitleText1('Calculus: Early Transcendentals')
   13 ## EditionText1('1')
   14 ## AuthorText1('Rogawski')
   15 ## Section1('2.1')
   16 ## Problem1('5')
   17 ## TitleText2('Calculus: Early Transcendentals')
   18 ## EditionText2('1')
   19 ## AuthorText2('Rogawski')
   20 ## Section2('2.1')
   21 ## Problem2('5')
   22 
   23 DOCUMENT();        # This should be the first executable line in the problem.
   24 
   25 loadMacros(
   26 "PG.pl",
   27 "PGbasicmacros.pl",
   28 "PGchoicemacros.pl",
   29 "PGanswermacros.pl",
   30 "PGauxiliaryFunctions.pl",
   31 "PGcourse.pl"
   32 );
   33 
   34 TEXT(beginproblem());
   35 $showPartialCorrectAnswers = 1;
   36 
   37 $v0 = random(40,100,5);
   38 $t0 = random(1,2,1);
   39 
   40 TEXT(EV2(<<EOT));
   41 If a ball is thrown straight up into the air with an initial
   42 velocity of \( $v0 \) ft/s, it height in feet after \( t \)
   43 second is given by \( y = $v0 t - 16 t^2 \).  Find the average
   44 velocity for the time period begining when \( t = $t0 \) and
   45 lasting  $BR (i) \( 0.1 \) seconds
   46 \{ans_rule(35) \} $BR
   47 $BR
   48 EOT
   49 
   50 $ans =$v0-32*$t0-16*0.1;
   51 ANS(num_cmp($ans));
   52 
   53 TEXT(EV2(<<EOT));
   54 (ii) \( 0.01 \) seconds
   55 \{ans_rule(35)  \} $BR
   56 $BR
   57 EOT
   58 
   59 $ans =$v0-32*$t0-16*0.01;
   60 ANS(num_cmp($ans));
   61 
   62 TEXT(EV2(<<EOT));
   63 (iii) \( 0.001 \) seconds
   64 \{ans_rule(35)  \} $BR
   65 $BR
   66 EOT
   67 
   68 $ans =$v0-32*$t0-16*0.001;
   69 ANS(num_cmp($ans));
   70 
   71 TEXT(EV2(<<EOT));
   72 Finally based on the above results, guess what the instantaneous
   73 velocity of the ball is when \( t =$t0 \).
   74 \{ans_rule(20) \}
   75 $BR
   76 EOT
   77 
   78 $ans =$v0-32*$t0;
   79 ANS(num_cmp($ans, relTol=>3));
   80 
   81 ENDDOCUMENT();        # This should be the last executable line in the problem.
   82