document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=320313>Question 320313</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 98. Height difference. 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?<BR>\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 #229408 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=229408\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> This same problem came up a few weeks ago, here is the response I made then<BR>\n" );
document.write( ":<BR>\n" );
document.write( "A red ball and a green ball are 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 after it is <BR>\n" );
document.write( "tossed is -16t^2 + 96t feet. <BR>\n" );
document.write( "The green ball is given an initial velocity of 80 feet per second and its height<BR>\n" );
document.write( " \"t\" seconds after being tossed is -16t^2 +80t feet.<BR>\n" );
document.write( ":<BR>\n" );
document.write( "a)Find a polynomial D(t) that represents the difference in the heights of the two balls.<BR>\n" );
document.write( "D(t) = (-16t^2 + 96t) - (-16t^2 +80t)<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Remove brackets<BR>\n" );
document.write( "D(t) = -16t^2 + 96t + 16t^2 - 80t<BR>\n" );
document.write( ":<BR>\n" );
document.write( "combine like terms:<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 balls are tossed?<BR>\n" );
document.write( "D(t) = 16(2)<BR>\n" );
document.write( "D(t) = 32 ft difference after 2 seconds<BR>\n" );
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document.write( "c)When does the difference in the heights stop increasing?<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Obviously, when one of the balls hits the ground<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Find when the lowest ball hits the ground (h=0)<BR>\n" );
document.write( "-16t^2 + 80t = 0<BR>\n" );
document.write( "Factor out -16t<BR>\n" );
document.write( "-16t(t - 5) = 0<BR>\n" );
document.write( "t = 5 seconds when the difference stops increasing;<BR>\n" );
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document.write( "A graph illustrates this well<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" );
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