document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=194477>Question 194477</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If an object is given an initial velocity of v0 feet per second from a height of s0 feet, then its height as a function of time is\r<BR>\n" );
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document.write( "h(t) = -16t^2 + v0t + s0\r<BR>\n" );
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document.write( "A potato gun is capable of launching a spud with an initial velocity of 80 feet per second. If the tater takes off from an elevation of 100 feet, how many seconds into its flight will it be at an elevation of 115 feet. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #145924 by </B><A HREF=/tutors/aboutme.mpl?userid=nerdybill><B>nerdybill(7384)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=nerdybill><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=nerdybill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=145924\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Simply plug in the given information into:<BR>\n" );
document.write( "h(t) = -16t^2 + v0t + s0 <BR>\n" );
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document.write( "h(t) = -16t^2 + v0t + s0 <BR>\n" );
document.write( "115 = -16t^2 + 80t + 100<BR>\n" );
document.write( "Moving all terms to the left:<BR>\n" );
document.write( "16t^2 - 80t + 15 = 0<BR>\n" );
document.write( "Solving the above using the quadratic equation yields:<BR>\n" );
document.write( "x = {4.805, 0.195}<BR>\n" );
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document.write( "The tater is at 115 ft at 0.195 secs and again at 4.805 secs after flight.<BR>\n" );
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document.write( "Details of quadratic follows:<BR>\n" );
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document.write( " <TR><TD  ALIGN=MIDDLE>Solved by <A  rel=nofollow HREF=http://wiki.algebra.com/index.php/Tutoring_-_pluggable_solvers>pluggable</A> solver: <A  rel=nofollow HREF=quadratic.solver>SOLVE quadratic equation with variable</A></TD></TR>\n" );
document.write( "<TR><TD  ALIGN=LEFT>Quadratic equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ax%5E2%2Bbx%2Bc=0 ALIGN=MIDDLE  ALT=\"ax%5E2%2Bbx%2Bc=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > (in our case <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16x%5E2%2B-80x%2B15+=+0 ALIGN=MIDDLE  ALT=\"16x%5E2%2B-80x%2B15+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >) has the following solutons:<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  For these solutions to exist, the <U>discriminant</U> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac ALIGN=MIDDLE  ALT=\"b%5E2-4ac\"   DISABLED_style= \"max-width:90%; height:auto;\" > should not be a negative number.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  First, we need to compute the discriminant <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac ALIGN=MIDDLE  ALT=\"b%5E2-4ac\"   DISABLED_style= \"max-width:90%; height:auto;\" >: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac=%28-80%29%5E2-4%2A16%2A15=5440 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%28-80%29%5E2-4%2A16%2A15=5440\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=5440 is greater than zero. That means that there are two solutions: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5B12%5D+=+%28--80%2B-sqrt%28+5440+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28--80%2B-sqrt%28+5440+%29%29%2F2%5Ca\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D+=+%28-%28-80%29%2Bsqrt%28+5440+%29%29%2F2%5C16+=+4.80488611432322 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%28-80%29%2Bsqrt%28+5440+%29%29%2F2%5C16+=+4.80488611432322\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B2%5D+=+%28-%28-80%29-sqrt%28+5440+%29%29%2F2%5C16+=+0.195113885676778 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%28-80%29-sqrt%28+5440+%29%29%2F2%5C16+=+0.195113885676778\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <BR>\n" );
document.write( "    Quadratic expression <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16x%5E2%2B-80x%2B15 ALIGN=MIDDLE  ALT=\"16x%5E2%2B-80x%2B15\"   DISABLED_style= \"max-width:90%; height:auto;\" > can be factored:<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16x%5E2%2B-80x%2B15+=+16%28x-4.80488611432322%29%2A%28x-0.195113885676778%29 ALIGN=MIDDLE  ALT=\"16x%5E2%2B-80x%2B15+=+16%28x-4.80488611432322%29%2A%28x-0.195113885676778%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 4.80488611432322, 0.195113885676778.\n" );
document.write( "Here's your graph:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+16%2Ax%5E2%2B-80%2Ax%2B15+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+16%2Ax%5E2%2B-80%2Ax%2B15+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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document.write( " </SPAN>\n" );
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