document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=299015>Question 299015</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A ball is thrown vertically upward from the top of a building 102 feet tall with an initial velocity of 60 feet per second. The distance s  (in feet) of the ball from the ground after  t seconds is s(t)=-16t^2+60t+102\r<BR>\n" );
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document.write( "What is the distance of the ball from the ground at time t=0?<BR>\n" );
document.write( "After how many seconds does the ball strike the ground?<BR>\n" );
document.write( "After how many seconds will the ball pass the top of the building on its way down?<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #215002 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=215002\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A ball is thrown vertically upward from the top of a building 102 feet tall with an initial velocity of 60 feet per second. The distance s (in feet) of the ball from the ground after t seconds is s(t)=-16t^2+60t+102<BR>\n" );
document.write( "What is the distance of the ball from the ground at time t=0?<BR>\n" );
document.write( "Set t=0 and plug into formula:<BR>\n" );
document.write( "s(t)=-16t^2+60t+102<BR>\n" );
document.write( "s(0)=-16*0^2+60(0)+102<BR>\n" );
document.write( "s(0)= 102 feet<BR>\n" );
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document.write( "After how many seconds does the ball strike the ground?<BR>\n" );
document.write( "Solve for t when s(t)=-102 (that's because we are 102 feet above the ground)<BR>\n" );
document.write( "s(t)=-16t^2+60t+102<BR>\n" );
document.write( "-102=-16t^2+60t+102<BR>\n" );
document.write( "0=-16t^2+60t+204<BR>\n" );
document.write( "0=-16t^2+60t+204<BR>\n" );
document.write( "0=-4t^2+15t+51<BR>\n" );
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document.write( "Solve using the quadratic formula.  Doing so yields:<BR>\n" );
document.write( "x = {-2.16, 5.91}<BR>\n" );
document.write( "Throw away the negative solution leaving:<BR>\n" );
document.write( "t = 5.91 seconds<BR>\n" );
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document.write( "After how many seconds will the ball pass the top of the building on its way down?<BR>\n" );
document.write( "Solve for t when s(t)=0<BR>\n" );
document.write( "s(t)=-16t^2+60t+102<BR>\n" );
document.write( "0=-16t^2+60t+102<BR>\n" );
document.write( "0=-8t^2+30t+51<BR>\n" );
document.write( "Solve using the quadratic formula (Details below).  Doing so yields:<BR>\n" );
document.write( "x = {-1.27, 5.02}<BR>\n" );
document.write( "Throw away the negative solution leaving:<BR>\n" );
document.write( "t = 5.02 seconds<BR>\n" );
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document.write( "Details of quadratic for part c:<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=-8x%5E2%2B30x%2B51+=+0 ALIGN=MIDDLE  ALT=\"-8x%5E2%2B30x%2B51+=+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=%2830%29%5E2-4%2A-8%2A51=2532 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%2830%29%5E2-4%2A-8%2A51=2532\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=2532 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+=+%28-30%2B-sqrt%28+2532+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28-30%2B-sqrt%28+2532+%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-%2830%29%2Bsqrt%28+2532+%29%29%2F2%5C-8+=+-1.26993640635228 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%2830%29%2Bsqrt%28+2532+%29%29%2F2%5C-8+=+-1.26993640635228\"   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-%2830%29-sqrt%28+2532+%29%29%2F2%5C-8+=+5.01993640635228 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%2830%29-sqrt%28+2532+%29%29%2F2%5C-8+=+5.01993640635228\"   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=-8x%5E2%2B30x%2B51 ALIGN=MIDDLE  ALT=\"-8x%5E2%2B30x%2B51\"   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=-8x%5E2%2B30x%2B51+=+-8%28x--1.26993640635228%29%2A%28x-5.01993640635228%29 ALIGN=MIDDLE  ALT=\"-8x%5E2%2B30x%2B51+=+-8%28x--1.26993640635228%29%2A%28x-5.01993640635228%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: -1.26993640635228, 5.01993640635228.\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+-8%2Ax%5E2%2B30%2Ax%2B51+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-8%2Ax%5E2%2B30%2Ax%2B51+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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