document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1190153>Question 1190153</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Bouncing Ball A ball is dropped from a height of 9 ft. The<BR>\n" );
document.write( "elasticity of the ball is such that it always bounces up one-<BR>\n" );
document.write( "third the distance it has fallen.<BR>\n" );
document.write( "(a) Find the total distance the ball has traveled at the instant<BR>\n" );
document.write( "it hits the ground the fifth time.<BR>\n" );
document.write( "(b) Find a formula for the total distance the ball has traveled<BR>\n" );
document.write( "at the instant it hits the ground the nth time. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #821754 by </B><A HREF=/tutors/aboutme.mpl?userid=Boreal><B>Boreal(15235)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Boreal><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=Boreal><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=821754\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> hits ground once: 9 feet<BR>\n" );
document.write( "bounces up 3 feet (12)<BR>\n" );
document.write( "bounces down 3 feet (15)<BR>\n" );
document.write( "bounces up 1 foot and back down 1 foot (17 feet) - has hit floor 3 times<BR>\n" );
document.write( "bounces up 1/3 foot and back down 1/3 foot (17 2/3 ft)- 4 times<BR>\n" );
document.write( "bounces up 1/9 foot and back down 1/9 foot (17 8/9) feet, the answer.<BR>\n" );
document.write( "-<BR>\n" );
document.write( "9+2*{3*(1/3)^0+3*(1/3)^1+3*(1/3)^2+3*(1/3)^3...}<BR>\n" );
document.write( "the infinite sum is 9+2*3/(1-1/3)=18 feet.<BR>\n" );
document.write( "The n th time is 9+ 2*9(1/3)*{{1-(1/3)^(n-1)/(1-(1/3)}, and when n=5, the answer is 17.89 or 17 (8/9).<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );