document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1115426>Question 1115426</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A flare is shot upward from the edge of a 88 foot tall cliff with an initial velocity of 82 ft/sec.  What is the maximum height above the ground this flare will go in feet? \r<BR>\n" );
document.write( "\n" );
document.write( "Round your answer to 1 decimal place. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #730297 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52787)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><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=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=730297\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
document.write( "A flare is shot upward from the edge of a 88 foot tall cliff with an initial velocity of 82 ft/sec.  <BR>\n" );
document.write( "What is the maximum height above the ground this flare will go in feet? <BR>\n" );
document.write( "Round your answer to 1 decimal place.<BR>\n" );
document.write( "~~~~~~~~~~~~~~~~~~~~~~~~~~~~\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<PRE STYLE=\"white-space: pre-wrap; white-space: -moz-pre-wrap; white-space: -pre-wrap; white-space: -o-pre-wrap; word-wrap: break-word;\">\r\n" );
document.write( "The formula for the height above the cliff base as the function of time is\r\n" );
document.write( "\r\n" );
document.write( "h(t) = -16t^2 + 82t + 88.     (1)\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "The height is maximum when the quadratic function (1) is maximum.\r\n" );
document.write( "\r\n" );
document.write( "It happens when  t = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-b%2F%282a%29 ALIGN=MIDDLE  ALT=\"-b%2F%282a%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-82%2F%282%2A%28-16%29%29 ALIGN=MIDDLE  ALT=\"-82%2F%282%2A%28-16%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=82%2F32 ALIGN=MIDDLE  ALT=\"82%2F32\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 2.56 seconds.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "At this time,  h(t) = -16*2.56^2 + 82*2.56 + 88 = 193.1 ft.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "<U>Answer</U>.  The maximum height above the cliff base is 193.1 ft.\r\n" );
document.write( "</PRE>\r<BR>\n" );
document.write( "\n" );
document.write( "-------------------<BR>\n" );
document.write( "On finding the maximum/minimum of a quadratic function see the lessons \r<BR>\n" );
document.write( "\n" );
document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/HOW-TO-complete-the-square-of-a-quadratic-function-to-find-its-minimum-maximum.lesson>HOW TO complete the square to find the minimum/maximum of a quadratic function</A>\r<BR>\n" );
document.write( "\n" );
document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/Briefly-on-How-to-complete-the-square-of-a-quadratic-function-to-find-its-minimum-maximum.lesson>Briefly on finding the minimum/maximum of a quadratic function</A>\r<BR>\n" );
document.write( "\n" );
document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/HOW-TO-complete-the-square-to-find-the-vertex-of-a-quadratic-function.lesson>HOW TO complete the square to find the vertex of a parabola</A>\r<BR>\n" );
document.write( "\n" );
document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/Briefly-on-finding-the-vertex-of-a-parabola.lesson>Briefly on finding the vertex of a parabola</A>\r<BR>\n" );
document.write( "\n" );
document.write( "in this site.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "To see other similar solved problems on a projectile thrown/shot/launched vertically up, &nbsp;look into the lessons\r<BR>\n" );
document.write( "\n" );
document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=https://www.algebra.com/algebra/homework/word/travel/Problem-on-a-projectile-moving-vertically.lesson>Problem on a projectile moving vertically up and down</A>\r<BR>\n" );
document.write( "\n" );
document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=https://www.algebra.com/algebra/homework/word/travel/Problem-on-projectile-shooted-vertically-upward.lesson>Problem on an arrow shot vertically upward</A>\r<BR>\n" );
document.write( "\n" );
document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=https://www.algebra.com/algebra/homework/word/travel/Typical-problems-on-an-projectile-moving-vertically-up-and-down.lesson>Problem on a ball thrown vertically up from the top of a tower</A> \r<BR>\n" );
document.write( "\n" );
document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=https://www.algebra.com/algebra/homework/word/travel/Problem-on-a-toy-rocket-launched-vertically-up--from-the-top-of-a-platform.lesson>Problem on a toy rocket launched vertically up from a tall platform</A>\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "=============\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "I wrote my text to fix an error in the @KMST calculation of the time to get the maximum height.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );