document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=191725>Question 191725</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/9780073533490/algebrahomeworkh>Elementary and Intermediate Algebra</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> A red ball and a green ball are<BR>\n" );
document.write( "simultaneously tossed into the air. The red ball is given an<BR>\n" );
document.write( "initial velocity of 96 feet per second, and its height t seconds<BR>\n" );
document.write( "after it is tossed is _16t2 _ 96t feet. The green ball<BR>\n" );
document.write( "is given an initial velocity of 80 feet per second, and its<BR>\n" );
document.write( "height t seconds after it is tossed is _16t2 _ 80t feet.<BR>\n" );
document.write( "a) Find a polynomial D(t) that represents the difference in<BR>\n" );
document.write( "the heights of the two balls.<BR>\n" );
document.write( "b) How much higher is the red ball 2 seconds after the<BR>\n" );
document.write( "balls are tossed?<BR>\n" );
document.write( "c) In reality, when does the difference in the heights stop<BR>\n" );
document.write( "increasing?\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #143851 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=143851\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A red ball and a green ball are<BR>\n" );
document.write( "simultaneously tossed into the air. The red ball is given an<BR>\n" );
document.write( "initial velocity of 96 feet per second, and its height t seconds<BR>\n" );
document.write( "after it is tossed is -16t2 + 96t feet. The green ball<BR>\n" );
document.write( "is given an initial velocity of 80 feet per second, and its<BR>\n" );
document.write( "height t seconds after it is tossed is -16t2 + 80t feet.<BR>\n" );
document.write( ";<BR>\n" );
document.write( " -16t^2 + 96t = h (redball)<BR>\n" );
document.write( "and<BR>\n" );
document.write( " -16t^2 + 80t = h (greenball)<BR>\n" );
document.write( "a) Find a polynomial D(t) that represents the difference in<BR>\n" );
document.write( "the heights of the two balls.<BR>\n" );
document.write( "D(t) = (-16t^2 + 96t) - (-16t^2 + 80t) <BR>\n" );
document.write( "Remove brackets<BR>\n" );
document.write( "D(t) = -16t^2 + 96t + 16t^2 - 80t <BR>\n" );
document.write( "D(t) = 16t<BR>\n" );
document.write( ":<BR>\n" );
document.write( "b) How much higher is the red ball 2 seconds after the<BR>\n" );
document.write( "balls are tossed?<BR>\n" );
document.write( "D(t) = 16(2)<BR>\n" );
document.write( "D(t) = 32 ft after 2 sec<BR>\n" );
document.write( ":<BR>\n" );
document.write( "c) In reality, when does the difference in the heights stop<BR>\n" );
document.write( "increasing? <BR>\n" );
document.write( "When the green ball hits the ground. h = 0<BR>\n" );
document.write( "If you solve -16t^2 + 80t = 0, you will find that will occur in 5 sec<BR>\n" );
document.write( ";<BR>\n" );
document.write( "Seen graphically; x axis is time in seconds, y axis is height in feet<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+200%2C+-4%2C+8%2C+-20%2C+150%2C+-16x%5E2%2B96x%2C+-16x%5E2%2B80x%29+ ALIGN=MIDDLE  ALT=\"+graph%28+300%2C+200%2C+-4%2C+8%2C+-20%2C+150%2C+-16x%5E2%2B96x%2C+-16x%5E2%2B80x%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >  </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );