document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=160577>Question 160577</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 98.) Height difference.  A red ball and a green ball are simultaneously tossed into the air.  The red ball is given an initial velocity of 96 feet per second, and its height t seconds after it is tossed is   feet.  The green ball is given an initial velocity of 80 feet per second, and its height t seconds after it is tosses is  feet.<BR>\n" );
document.write( "a.) Find the polynomial D(t) that represents the difference in the height of the two balls.<BR>\n" );
document.write( "b.) How much higher is the red ball 2 seconds after the balls are tossed?<BR>\n" );
document.write( "c.) In reality, when does the difference in the heights stop increasing?<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #118442 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=118442\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Height difference. A red ball and a green ball are simultaneously tossed into the air. The red ball is given an initial velocity of 96 feet per second, and its height t seconds after it is tossed is feet. The green ball is given an initial velocity of 80 feet per second, and its height t seconds after it is tosses is feet.<BR>\n" );
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document.write( "h = height<BR>\n" );
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document.write( "Red Ball equation:<BR>\n" );
document.write( "h = -16t^2 + 96t<BR>\n" );
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document.write( "Green Ball equation<BR>\n" );
document.write( "h = -16t^2 + 80t<BR>\n" );
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document.write( "a.) Find the polynomial D(t) that represents the difference in the height of the two balls.<BR>\n" );
document.write( "......Red ball height - green ball height<BR>\n" );
document.write( "D(t) = (-16t^2 + 96t) - (-16t^2 + 80t)<BR>\n" );
document.write( "D(t) = -16t^2 + 96t + 16t^2 - 80t; removing the brackets changes the signs<BR>\n" );
document.write( "D(t) = -16t^2 + 16t^2 +96t - 80t<BR>\n" );
document.write( "D(t) = 16t<BR>\n" );
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document.write( "b.) How much higher is the red ball 2 seconds after the balls are tossed?<BR>\n" );
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document.write( "Replace t with 2 sec: 16(2) = 32 ft<BR>\n" );
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document.write( "c.) In reality, when does the difference in the heights stop increasing?<BR>\n" );
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document.write( "After 5 sec, Green ball hits the ground in 5 sec<BR>\n" );
document.write( "You can see this: <BR>\n" );
document.write( "h = -16(25) + 80(5) <BR>\n" );
document.write( "h = -400 + 400<BR>\n" );
document.write( "h = 0<BR>\n" );
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document.write( "Here's a graphical representation of the two balls<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;\" ><BR>\n" );
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document.write( "</TD></TR></TABLE>\n" );