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Fixed formatting and TeX errors in solution
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OpenProblemLibrary/ma122DB/set10/s4_10_75.pg

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Original file line numberDiff line numberDiff line change
@@ -44,7 +44,7 @@ Answer: \{ans_rule(30) \}
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END_TEXT
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$t1 = -$v1/32;
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$ans = "$v1*$v1/64";
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$ans = $v1*$v1/64;
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ANS(num_cmp($ans));
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@@ -55,10 +55,10 @@ position at time \( t \) (\( s(t) \)), instantaneous velocity
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at time \( t \) (\( v(t) \)), and acceleration at time \( t\) (\(a(t)\)).
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This relationship is given by:
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$BR$BR
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\[ \begin{array}
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v(t) = s'(t) \\
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a(t) = v'(t) = s''(t) \\
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\end{array}
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\[ \begin{split}
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v(t) &= s'(t) \\
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a(t) &= v'(t) = s''(t) \\
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\end{split}
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\]
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$BR$BR
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With this in mind, this problem becomes an exercise in finding
@@ -92,11 +92,11 @@ and we know the stone struck the ground (so its position was 0) at
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\( t = !{$t1:%5.3f} \), we can solve the following equation for \( C_2 \).
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$BR$BR
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\[
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\begin{array}
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s(!{$t1:%5.3f}) = 0 \\
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-16(!{$t1:%5.3f})^2 + C_2 = 0 \\
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C_2 = !{$ans:%5.3f} \\
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\end{array}
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\begin{split}
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s(!{$t1:%5.3f}) &= 0 \\
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-16(!{$t1:%5.3f})^2 + C_2 &= 0 \\
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C_2 &= !{$ans:%5.3f} \\
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\end{split}
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\]
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Now, since we want to know the height from which the stone was dropped, we
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just need to find its position at time \( t = 0 \). But this is \( s(0) = -16(0)^2+ $ans \)

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