document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1173712>Question 1173712</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A ferris wheel is 35 meters in diameter and boarded from a platform that is 2 meters above the ground. The six o'clock position on the ferris wheel is level with the loading platform. The wheel completes 1 full revolution in 6 minutes. The function h = f(t) gives your height in meters above the ground t minutes after the wheel begins to turn.\r<BR>\n" );
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document.write( "What is the Amplitude? ? meters<BR>\n" );
document.write( "What is the Midline? y = ? meters <BR>\n" );
document.write( "What is the Period? ? minutes <BR>\n" );
document.write( "How High are you off of the ground after 3 minutes? ? meters </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #799002 by </B><A HREF=/tutors/aboutme.mpl?userid=htmentor><B>htmentor(1343)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=htmentor><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=htmentor><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=799002\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The general form for the height of the Ferris wheel as a function of time is:<BR>\n" );
document.write( "h(t) = Acos(wt) + h0, where h0 is the midline, A is the amplitude, and w = the angular speed in radians per minute. <BR>\n" );
document.write( "h(t) oscillates about the midline with an amplitude equal to the radius of the wheel. <BR>\n" );
document.write( "The midline, i.e. halfway up, is given by the radius plus h0 = 19.5 m<BR>\n" );
document.write( "Thus the amplitude is equal to 17.5 m. Since the initial height must be 2 m, <BR>\n" );
document.write( "we have A = -17.5. The angular speed is 2*pi radians per 6 min = pi/3 rad/min.<BR>\n" );
document.write( "Thus the equation describing the height is h(t) = -17.5*cos((pi/3)*t) + 19.5<BR>\n" );
document.write( "The period, T is given by 2pi/w = 2pi/(pi/3) = 6 min. <BR>\n" );
document.write( "h(3) = -17.5*cos(pi) + 19.5 = 17.5 + 19.5 = 37 m (maximum height)<BR>\n" );
document.write( "A graph of the function is attached.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/display-illustration.mpl?tutor=htmentor&illustration_name=FW.png\"> </SPAN>\n" );
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