##DESCRIPTION
##  Find the velocity of a ball thrown straight up during periods of time
##  approaching a value, then guess the instantaneous velocity at that point
##ENDDESCRIPTION

##KEYWORDS('Calculus')
##Tagged by ynw2d

##DBsubject('Calculus')
##DBchapter('Limits and Derivatives')
## DBsection('Tangents, Velocities, and Other Rates of Change')
## TitleText1('Calculus: Early Transcendentals')
## EditionText1('1')
## AuthorText1('Rogawski')
## Section1('2.1')
## Problem1('5')
## TitleText2('Calculus: Early Transcendentals')
## EditionText2('1')
## AuthorText2('Rogawski')
## Section2('2.1')
## Problem2('5')

DOCUMENT();        # This should be the first executable line in the problem.

loadMacros(
"PG.pl",
"PGbasicmacros.pl",
"PGchoicemacros.pl",
"PGanswermacros.pl",
"PGauxiliaryFunctions.pl",
"PGcourse.pl"
);

TEXT(beginproblem());
$showPartialCorrectAnswers = 1;

$v0 = random(40,100,5);
$t0 = random(1,2,1);

TEXT(EV2(<<EOT));
If a ball is thrown straight up into the air with an initial
velocity of \( $v0 \) ft/s, it height in feet after \( t \)
second is given by \( y = $v0 t - 16 t^2 \).  Find the average
velocity for the time period begining when \( t = $t0 \) and
lasting  $BR (i) \( 0.1 \) seconds
\{ans_rule(35) \} $BR
$BR
EOT

$ans =$v0-32*$t0-16*0.1;
ANS(num_cmp($ans));

TEXT(EV2(<<EOT));
(ii) \( 0.01 \) seconds
\{ans_rule(35)  \} $BR
$BR
EOT

$ans =$v0-32*$t0-16*0.01;
ANS(num_cmp($ans));

TEXT(EV2(<<EOT));
(iii) \( 0.001 \) seconds
\{ans_rule(35)  \} $BR
$BR
EOT

$ans =$v0-32*$t0-16*0.001;
ANS(num_cmp($ans));

TEXT(EV2(<<EOT));
Finally based on the above results, guess what the instantaneous
velocity of the ball is when \( t =$t0 \).
\{ans_rule(20) \}
$BR
EOT

$ans =$v0-32*$t0;
ANS(num_cmp($ans, relTol=>3));

ENDDOCUMENT();        # This should be the last executable line in the problem.