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| 1 : | jj | 143 | ##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 : | jjholt | 314 | ##KEYWORDS('Calculus') |
| 7 : | ##Tagged by ynw2d | ||
| 8 : | jj | 143 | |
| 9 : | jjholt | 314 | ##DBsubject('Calculus') |
| 10 : | ##DBchapter('Limits and Derivatives') | ||
| 11 : | jjholt | 446 | ## DBsection('Tangents, Velocities, and Other Rates of Change') |
| 12 : | sh002i | 556 | ## 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 : | jjholt | 314 | |
| 23 : | jj | 143 | 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 : | gage | 1316 | "PGauxiliaryFunctions.pl", |
| 31 : | "PGcourse.pl" | ||
| 32 : | jj | 143 | ); |
| 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 : |
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