document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=211112>Question 211112</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A particle undergoes two displacements. The<BR>\n" );
document.write( "first has a magnitude of 11 m and makes an<BR>\n" );
document.write( "angle of 76&#9702; with the positive x axis.<BR>\n" );
document.write( "The result after the two displacements is<BR>\n" );
document.write( "8.7 m directed at an angle of 109 &#9702; to the<BR>\n" );
document.write( "positive x axis using counter-clockwise as the<BR>\n" );
document.write( "positive angular direction (see the figure be-<BR>\n" );
document.write( "low).<BR>\n" );
document.write( "Find the magnitude of the second displace-<BR>\n" );
document.write( "ment. Answer in units of m. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #159630 by </B><A HREF=/tutors/aboutme.mpl?userid=RAY100><B>RAY100(1637)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=RAY100><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=159630\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The  first  displacement<BR>\n" );
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document.write( "delta x = 11  cos 76 = 2.661<BR>\n" );
document.write( "delta  y =11  sin 76 = 10.67<BR>\n" );
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document.write( "The  final  displacement<BR>\n" );
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document.write( "delta  x = 8.7 cos 109  = -2.832<BR>\n" );
document.write( "delta  y = 8.7 sin 109  = 8.23<BR>\n" );
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document.write( "The  second  displacement<BR>\n" );
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document.write( "delta  x = -2.832-2.661 = -5.493<BR>\n" );
document.write( "delta  y = 8.23 - 10.67 = -2.44<BR>\n" );
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document.write( "Magnitude  of  2nd  displacement = sqrt{ 5.493^2 +2.44^2 } = 6.01 m<BR>\n" );
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document.write( "A  rough  sketch  helps  visualize vectors<BR>\n" );
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document.write( "   </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );