document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=132785>Question 132785</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/9780534404512/algebrahomeworkh>Fundamentals of Algebric Modeling</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> An object is shot upward from a height of 96 feet with an intial velocity of 48 feet per second. Its height (h) above the ground in feet after t seconds is given by the formula\r<BR>\n" );
document.write( "\n" );
document.write( "h = 16t^2 + 48t + 96 at what times will the object be 128 feet above the ground? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #97034 by </B><A HREF=/tutors/aboutme.mpl?userid=nycsharkman><B>nycsharkman(136)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=nycsharkman><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=97034\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> An object is shot upward from a height of 96 feet with an intial velocity of 48 feet per second. Its height (h) above the ground in feet after t seconds is given by the formula\r<BR>\n" );
document.write( "\n" );
document.write( "h = 16t^2 + 48t + 96 at what times will the object be 128 feet above the ground?\r<BR>\n" );
document.write( "\n" );
document.write( "Let h = 128 feet above ground.\r<BR>\n" );
document.write( "\n" );
document.write( "Then, 128 = 16t^2 + 48t + 96 \r<BR>\n" );
document.write( "\n" );
document.write( "We are looking for t.\r<BR>\n" );
document.write( "\n" );
document.write( "So, let t = the time it will take the object to reach 128 feet above the rgound.\r<BR>\n" );
document.write( "\n" );
document.write( "16t^2 + 48t + 96 - 128 = 0\r<BR>\n" );
document.write( "\n" );
document.write( "16t^2 + 48t -32 = 0....This is a quadratic equation.\r<BR>\n" );
document.write( "\n" );
document.write( "I really hate those big coefficient numbers.  Do you see 16, 48 and 32?\r<BR>\n" );
document.write( "\n" );
document.write( "Let's remove them!\r<BR>\n" );
document.write( "\n" );
document.write( "I will divide all of them (including 0 on the right side) by 16, which is the coefficient of t^2.\r<BR>\n" );
document.write( "\n" );
document.write( "Doing so, I get a simplified form of the quadratic equation:\r<BR>\n" );
document.write( "\n" );
document.write( "t^2 + 3t -2 = 0....This is much easier to work with, right?\r<BR>\n" );
document.write( "\n" );
document.write( "We factor the left side of the equation, if possible.\r<BR>\n" );
document.write( "\n" );
document.write( "This quadratic equation is not factorable.\r<BR>\n" );
document.write( "\n" );
document.write( "This means we must use the quadratic formula.\r<BR>\n" );
document.write( "\n" );
document.write( "I assume that you know how to use it, right?\r<BR>\n" );
document.write( "\n" );
document.write( "t = -b+ -sqrt{b^2 - 4ac})/2a, where a = 1, b = 3 and c = -2.\r<BR>\n" );
document.write( "\n" );
document.write( "Plug and chug.\r<BR>\n" );
document.write( "\n" );
document.write( "t = -3+ - sqrt{3^2 - 4(1)(-2)}/2(1)\r<BR>\n" );
document.write( "\n" );
document.write( "t = -3 + -sqrt{9 + 8}/2\r<BR>\n" );
document.write( "\n" );
document.write( "t = -3 + -sqrt{17}/2\r<BR>\n" );
document.write( "\n" );
document.write( "We now separate t into two sections: a positive section and a negative section.\r<BR>\n" );
document.write( "\n" );
document.write( "t = -3 + sqrt{17}/2\r<BR>\n" );
document.write( "\n" );
document.write( "t = 0.561552813\r<BR>\n" );
document.write( "\n" );
document.write( "The time it will take the object to reach 128 feet above the ground is about 0.6 seconds.  I rounded to the tenths place.\r<BR>\n" );
document.write( "\n" );
document.write( "===================\r<BR>\n" );
document.write( "\n" );
document.write( "t = -3 - sqrt{17}/2\r<BR>\n" );
document.write( "\n" );
document.write( "t = -3.561552813....This answer is rejected because we are dealing with measure of time, which always moves forward not backward and thus will always be positve.\r<BR>\n" );
document.write( "\n" );
document.write( "Make sense?\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );