document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=211170>Question 211170</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Ths is a summer math problem I was assigned to complete. A punter can kick a football with an initial velocity of 48 feet per second. How many seconds will it take for the ball to return to the ground?(Hint: Use the formula h=vt-16t2*)I was unsure whether or not this formula was correct for some reason I thought the formula was h=v-16t2*. I still need help wth completing the problem though. Thank you in adance the sooner this is answered the better.\r<BR>\n" );
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document.write( "*The 2 in the problems above is a square. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #159535 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=159535\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=vt-16t%5E2 ALIGN=MIDDLE  ALT=\"h=vt-16t%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given formula\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=48t-16t%5E2 ALIGN=MIDDLE  ALT=\"h=48t-16t%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in the given velocity of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=v=48 ALIGN=MIDDLE  ALT=\"v=48\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=48t-16t%5E2 ALIGN=MIDDLE  ALT=\"0=48t-16t%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in the height of 0 <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=0 ALIGN=MIDDLE  ALT=\"h=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > (since the height is zero at the ground)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=-16t%5E2%2B48t ALIGN=MIDDLE  ALT=\"0=-16t%5E2%2B48t\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rearrange the terms.\r<BR>\n" );
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document.write( "Notice that the quadratic <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-16t%5E2%2B48t ALIGN=MIDDLE  ALT=\"-16t%5E2%2B48t\"   DISABLED_style= \"max-width:90%; height:auto;\" > is in the form of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=At%5E2%2BBt%2BC ALIGN=MIDDLE  ALT=\"At%5E2%2BBt%2BC\"   DISABLED_style= \"max-width:90%; height:auto;\" > where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=-16 ALIGN=MIDDLE  ALT=\"A=-16\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=B=48 ALIGN=MIDDLE  ALT=\"B=48\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C=0 ALIGN=MIDDLE  ALT=\"C=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Let's use the quadratic formula to solve for \"t\":\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%28-B+%2B-+sqrt%28+B%5E2-4AC+%29%29%2F%282A%29 ALIGN=MIDDLE  ALT=\"t+=+%28-B+%2B-+sqrt%28+B%5E2-4AC+%29%29%2F%282A%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the quadratic formula\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%28-%2848%29+%2B-+sqrt%28+%2848%29%5E2-4%28-16%29%280%29+%29%29%2F%282%28-16%29%29 ALIGN=MIDDLE  ALT=\"t+=+%28-%2848%29+%2B-+sqrt%28+%2848%29%5E2-4%28-16%29%280%29+%29%29%2F%282%28-16%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=-16 ALIGN=MIDDLE  ALT=\"A=-16\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=B=48 ALIGN=MIDDLE  ALT=\"B=48\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C=0 ALIGN=MIDDLE  ALT=\"C=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%28-48+%2B-+sqrt%28+2304-4%28-16%29%280%29+%29%29%2F%282%28-16%29%29 ALIGN=MIDDLE  ALT=\"t+=+%28-48+%2B-+sqrt%28+2304-4%28-16%29%280%29+%29%29%2F%282%28-16%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=48 ALIGN=MIDDLE  ALT=\"48\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2304 ALIGN=MIDDLE  ALT=\"2304\"   DISABLED_style= \"max-width:90%; height:auto;\" >. \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%28-48+%2B-+sqrt%28+2304-0+%29%29%2F%282%28-16%29%29 ALIGN=MIDDLE  ALT=\"t+=+%28-48+%2B-+sqrt%28+2304-0+%29%29%2F%282%28-16%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%28-16%29%280%29 ALIGN=MIDDLE  ALT=\"4%28-16%29%280%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%28-48+%2B-+sqrt%28+2304+%29%29%2F%282%28-16%29%29 ALIGN=MIDDLE  ALT=\"t+=+%28-48+%2B-+sqrt%28+2304+%29%29%2F%282%28-16%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" > from <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2304 ALIGN=MIDDLE  ALT=\"2304\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2304 ALIGN=MIDDLE  ALT=\"2304\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%28-48+%2B-+sqrt%28+2304+%29%29%2F%28-32%29 ALIGN=MIDDLE  ALT=\"t+=+%28-48+%2B-+sqrt%28+2304+%29%29%2F%28-32%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-16 ALIGN=MIDDLE  ALT=\"-16\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-32 ALIGN=MIDDLE  ALT=\"-32\"   DISABLED_style= \"max-width:90%; height:auto;\" >. \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%28-48+%2B-+48%29%2F%28-32%29 ALIGN=MIDDLE  ALT=\"t+=+%28-48+%2B-+48%29%2F%28-32%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Take the square root of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2304 ALIGN=MIDDLE  ALT=\"2304\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=48 ALIGN=MIDDLE  ALT=\"48\"   DISABLED_style= \"max-width:90%; height:auto;\" >. \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%28-48+%2B+48%29%2F%28-32%29 ALIGN=MIDDLE  ALT=\"t+=+%28-48+%2B+48%29%2F%28-32%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%28-48+-+48%29%2F%28-32%29 ALIGN=MIDDLE  ALT=\"t+=+%28-48+-+48%29%2F%28-32%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Break up the expression. \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%280%29%2F%28-32%29 ALIGN=MIDDLE  ALT=\"t+=+%280%29%2F%28-32%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=++%28-96%29%2F%28-32%29 ALIGN=MIDDLE  ALT=\"t+=++%28-96%29%2F%28-32%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms. \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+0 ALIGN=MIDDLE  ALT=\"t+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+3 ALIGN=MIDDLE  ALT=\"t+=+3\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify. \r<BR>\n" );
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document.write( "So the solutions are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+0 ALIGN=MIDDLE  ALT=\"t+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+3 ALIGN=MIDDLE  ALT=\"t+=+3\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "This means that at times of 0 and 3 seconds, the ball will be at the ground. \r<BR>\n" );
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document.write( "Since we already know that the ball is at the ground at 0 seconds, the other solution <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=3 ALIGN=MIDDLE  ALT=\"t=3\"   DISABLED_style= \"max-width:90%; height:auto;\" > is more interesting. So we're going to ignore <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=0 ALIGN=MIDDLE  ALT=\"t=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Answer:\r<BR>\n" );
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document.write( "So it will take 3 seconds for the ball to return to the ground. </SPAN>\n" );
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