document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1182930>Question 1182930</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A narrow arch supporting a stone bridge is in the shape of half an ellipse and is 36 m long and 14 m high. A person standing at one focus plays with a ball by throwing it against the arch. The ball always bounces off the arch once and strikes the same point on the ground (the other focus).<BR>\n" );
document.write( "a. How far apart are the person throwing a ball and a point on the ground at which the ball strikes?<BR>\n" );
document.write( "b. What is the height of the arch exactly below the position of the person? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #813056 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52784)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><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=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=813056\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
document.write( "A narrow arch supporting a stone bridge is in the shape of half an ellipse and is 36 m long and 14 m high. <BR>\n" );
document.write( "A person standing at one focus plays with a ball by throwing it against the arch. <BR>\n" );
document.write( "The ball always bounces off the arch once and strikes the same point on the ground (the other focus).<BR>\n" );
document.write( "a. How far apart are the person throwing a ball and a point on the ground at which the ball strikes?<BR>\n" );
document.write( "b. What is the height of the arch exactly below the position of the person?<BR>\n" );
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document.write( "The semi-axes are  a = 36/2 = 18 meters (the major semi-axis) and b = 14 meters (the minor semi-axis).\r\n" );
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document.write( "Hence, the distance from the focus to the center of the ellipse is\r\n" );
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document.write( "    c = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28a%5E2+-+b%5E2%29 ALIGN=MIDDLE  ALT=\"sqrt%28a%5E2+-+b%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2818%5E2+-+14%5E2%29 ALIGN=MIDDLE  ALT=\"sqrt%2818%5E2+-+14%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 11.314 m.\r\n" );
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document.write( "The distance between the focuses is twice this value, i.e.  2*11.314 = 22.628 meters.    <U>ANSWER</U>\r\n" );
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document.write( "For info about the elements of an ellipse, see the lesson\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=http://www.algebra.com/algebra/homework/Quadratic-relations-and-conic-sections/Ellipse-definition--canonical-equation--characteristic-points-and-elements.lesson>Ellipse definition, canonical equation, characteristic points and elements</A> \r<BR>\n" );
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document.write( "in this site.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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