document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=262846>Question 262846</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I do not know where to start. <BR>\n" );
document.write( "A red ball and a green ball are simultaneously tossed into the air.<BR>\n" );
document.write( "Find a polynomial D(t) that represents the difference in the heights of the two balls. The red ball is given an initial velocity of 96 feet per second, and its height t seconds after it is tossed is -16t^2 + 96t feet. The green ball is given an initial velocity of 80feet per second, and its height t second, and its height t seconds after it is tossed is -16t^ + 80t feet. How much higher is the red ball 2 seconds after the balls are tossed? In reality, when does the difference in the heights stop increasing? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #193630 by </B><A HREF=/tutors/aboutme.mpl?userid=drk><B>drk(1908)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=drk><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=193630\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Lets look at the red ball equation as<BR>\n" );
document.write( "(i) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%28t%29+=+-16t%5E2+%2B+96t ALIGN=MIDDLE  ALT=\"h%28t%29+=+-16t%5E2+%2B+96t\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "we want to express this in vertex form to get the max ht. in vertex form the red ball is<BR>\n" );
document.write( "(ii) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%28t%29+=+-16%28t-3%29%5E2+%2B+144 ALIGN=MIDDLE  ALT=\"h%28t%29+=+-16%28t-3%29%5E2+%2B+144\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "this tells us that (1) it is a parabola opening down; (2) after 3 seconds a max ht occurs at 144 feet.<BR>\n" );
document.write( "t= 2 gives us<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%282%29+=+-16%282-3%29%5E2+%2B+144 ALIGN=MIDDLE  ALT=\"h%282%29+=+-16%282-3%29%5E2+%2B+144\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%282%29+=+128+ft. ALIGN=MIDDLE  ALT=\"h%282%29+=+128+ft.\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "--------<BR>\n" );
document.write( "Lets look at the green ball equation as<BR>\n" );
document.write( "(i) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%28t%29+=+-16t%5E2+%2B+80t ALIGN=MIDDLE  ALT=\"h%28t%29+=+-16t%5E2+%2B+80t\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "we want to express this in vertex form to get the max ht. in vertex form the green ball is<BR>\n" );
document.write( "(ii) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%28t%29+=+-16%28t-2.5%29%5E2+%2B+100 ALIGN=MIDDLE  ALT=\"h%28t%29+=+-16%28t-2.5%29%5E2+%2B+100\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "this tells us that (1) it is a parabola opening down; (2) after 2.5 seconds a max ht occurs at 100 feet.<BR>\n" );
document.write( "t= 2 gives us<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%282%29+=+-16%282-2.5%29%5E2+%2B+100 ALIGN=MIDDLE  ALT=\"h%282%29+=+-16%282-2.5%29%5E2+%2B+100\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%282%29+=+96+ft. ALIGN=MIDDLE  ALT=\"h%282%29+=+96+ft.\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "--------<BR>\n" );
document.write( "Since the red ball had a great initial velocity, we have the difference formula as<BR>\n" );
document.write( "D(t) = red ball equation - green ball equation<BR>\n" );
document.write( "or<BR>\n" );
document.write( "D(t) = -16(t-3)^2 + 144 - (-16(t-2.5)^2 + 100))<BR>\n" );
document.write( "--------<BR>\n" );
document.write( "after 2 seconds, the red ball is 32 feet higher than the green ball.<BR>\n" );
document.write( "--------<BR>\n" );
document.write( "the difference in heights will always be increasing </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );