document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1205132>Question 1205132</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A pendulum is connected to a rope 3 m long, which is connected to a ceiling 4 m high. The angle between its widest swing and vertical hanging position is π/3. If the pendulum swings out to its widest position in 2 seconds, model the height of the pendulum from the ground using a cosine function, considering vertical to be t = 0.\r<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 #841779 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=841779\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> a rope <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3m+ ALIGN=MIDDLE  ALT=\"3m+\"   DISABLED_style= \"max-width:90%; height:auto;\" >long<BR>\n" );
document.write( " a ceiling <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4m ALIGN=MIDDLE  ALT=\"4m\"   DISABLED_style= \"max-width:90%; height:auto;\" > high\r<BR>\n" );
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document.write( "so, from the floor to the pendulum is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1m+ ALIGN=MIDDLE  ALT=\"1m+\"   DISABLED_style= \"max-width:90%; height:auto;\" >=> minimum height \r<BR>\n" );
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document.write( "the vertical distance to the ceiling is :\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=3m%2Acos%28alpha%29+ ALIGN=MIDDLE  ALT=\"h=3m%2Acos%28alpha%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "since the highest angle is just <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=alpha=+pi%2F3+ ALIGN=MIDDLE  ALT=\"alpha=+pi%2F3+\"   DISABLED_style= \"max-width:90%; height:auto;\" >and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%28pi%2F3%29+=+1%2F2 ALIGN=MIDDLE  ALT=\"cos%28pi%2F3%29+=+1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, the smallest distance to the ceiling is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=3m%2A%281%2F2%29+=+1.5m+ ALIGN=MIDDLE  ALT=\"h=3m%2A%281%2F2%29+=+1.5m+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "and <BR>\n" );
document.write( "the highest point is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%5B1%5D=1m%2B1.5m=2.5m ALIGN=MIDDLE  ALT=\"h%5B1%5D=1m%2B1.5m=2.5m\"   DISABLED_style= \"max-width:90%; height:auto;\" > from the ground \r<BR>\n" );
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document.write( "then, cosine function will be:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%28t%29=D-Acos%28Bt%29 ALIGN=MIDDLE  ALT=\"h%28t%29=D-Acos%28Bt%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "range of the pendulum's height above the ground is \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%3C=+h%28t%29+%3C=+2.5 ALIGN=MIDDLE  ALT=\"1%3C=+h%28t%29+%3C=+2.5\"   DISABLED_style= \"max-width:90%; height:auto;\" >, where \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%280%29=1 ALIGN=MIDDLE  ALT=\"h%280%29=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%282%29=2.5 ALIGN=MIDDLE  ALT=\"h%282%29=2.5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%284%29=1 ALIGN=MIDDLE  ALT=\"h%284%29=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "amplitude is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=%282.5-1%29%2F2=0.75 ALIGN=MIDDLE  ALT=\"A=%282.5-1%29%2F2=0.75\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "midline is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D=%281%2B2.5%29%2F2=1.75 ALIGN=MIDDLE  ALT=\"D=%281%2B2.5%29%2F2=1.75\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "the period is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=T=4+ ALIGN=MIDDLE  ALT=\"T=4+\"   DISABLED_style= \"max-width:90%; height:auto;\" >=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=B=2pi%2FT=2pi%2F4=pi%2F2 ALIGN=MIDDLE  ALT=\"B=2pi%2FT=2pi%2F4=pi%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "and, function is:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%28t%29=1.75-0.75%2Acos%28%28pi%2F2%29%2At%29 ALIGN=MIDDLE  ALT=\"h%28t%29=1.75-0.75%2Acos%28%28pi%2F2%29%2At%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "​\r<BR>\n" );
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