document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=194403>Question 194403</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A swimmer is about to dive into a pool from the end of a diving board that is 24 feet above the waters surface. if he springs up from the board at a speed of 8 feet per second, when will he hit the water? what will be his maximum height above the water? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #145869 by </B><A HREF=/tutors/aboutme.mpl?userid=Earlsdon><B>Earlsdon(6294)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Earlsdon><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=145869\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> You can use the equation for the height of an object propelled upwards from an initial height (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%5B0%5D ALIGN=MIDDLE  ALT=\"h%5B0%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >) with an initial velocity (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=v%5B0%5D ALIGN=MIDDLE  ALT=\"v%5B0%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >):<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%28t%29+=+%281%2F2%29gt%5E2%2Bv%5B0%5Dt%2Bh%5B0%5D ALIGN=MIDDLE  ALT=\"h%28t%29+=+%281%2F2%29gt%5E2%2Bv%5B0%5Dt%2Bh%5B0%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > where g is the acceleration due to gravity, 32 ft/sec. sq. Making the appropriate substitutions:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%28t%29+=+-16t%5E2%2B8t%2B24 ALIGN=MIDDLE  ALT=\"h%28t%29+=+-16t%5E2%2B8t%2B24\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "To find the time the diver hits the water means to find the time (t) at which his height (h) is zero.<BR>\n" );
document.write( "1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-16t%5E2%2B8t%2B24+=+0 ALIGN=MIDDLE  ALT=\"-16t%5E2%2B8t%2B24+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor out -8.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-8%282t%5E2-t-3%29+=+0 ALIGN=MIDDLE  ALT=\"-8%282t%5E2-t-3%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Now factor the trinomial.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2t%5E2-t-3+=+%282t-3%29%28t%2B1%29 ALIGN=MIDDLE  ALT=\"2t%5E2-t-3+=+%282t-3%29%28t%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" > So...<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2t-3%29+=+0 ALIGN=MIDDLE  ALT=\"2t-3%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%2B1+=+0 ALIGN=MIDDLE  ALT=\"t%2B1+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > and...<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+3%2F2 ALIGN=MIDDLE  ALT=\"t+=+3%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+-1 ALIGN=MIDDLE  ALT=\"t+=+-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Discard the negative solution as the time will be a positive value.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+3%2F2 ALIGN=MIDDLE  ALT=\"t+=+3%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The diver will hit the water in 1.5 seconds.<BR>\n" );
document.write( "His maximum height can be found by finding the coordinates of the vertex (a maximum) of the downward-opening parabola represented by the quadratic equation.<BR>\n" );
document.write( "The t-value is given by:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+-b%2F2a ALIGN=MIDDLE  ALT=\"t+=+-b%2F2a\"   DISABLED_style= \"max-width:90%; height:auto;\" > and a = -16, b = 8.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%28-8%29%2F2%28-16%29 ALIGN=MIDDLE  ALT=\"t+=+%28-8%29%2F2%28-16%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+1%2F4 ALIGN=MIDDLE  ALT=\"t+=+1%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >seconds. Now substitute this value of t into equation 1) above and solve for h.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%281%2F4%29+=+-16%281%2F4%29%5E2%2B8%281%2F4%29%2B24 ALIGN=MIDDLE  ALT=\"h%281%2F4%29+=+-16%281%2F4%29%5E2%2B8%281%2F4%29%2B24\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%281%2F4%29+=+-16%281%2F16%29%2B%288%2F4%29%2B24 ALIGN=MIDDLE  ALT=\"h%281%2F4%29+=+-16%281%2F16%29%2B%288%2F4%29%2B24\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%281%2F4%29+=+-1%2B2%2B24 ALIGN=MIDDLE  ALT=\"h%281%2F4%29+=+-1%2B2%2B24\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%281%2F4%29+=+25 ALIGN=MIDDLE  ALT=\"h%281%2F4%29+=+25\"   DISABLED_style= \"max-width:90%; height:auto;\" >feet.<BR>\n" );
document.write( "The diver attains a maximum height of 25 feet above the water. <BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );