document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1200933>Question 1200933</A>: <I><SPAN STYLE=\"word-break: break-all;\"> a) In this question, i is a unit vector due east and j is a unit vector due north. <BR>\n" );
document.write( " A cyclist rides at a speed of 4ms−1 on a bearing of 015°. Write the velocity vector of the cyclist in <BR>\n" );
document.write( "the form xi + yj, where x and y are constants. [2] <BR>\n" );
document.write( "(b) A vector of magnitude 6 on a bearing of 300° is added to a vector of magnitude 2 on a bearing of <BR>\n" );
document.write( "230° to give a vector v. Find the magnitude and bearing of v.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #835225 by </B><A HREF=/tutors/aboutme.mpl?userid=Alan3354><B>Alan3354(69443)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Alan3354><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=Alan3354><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=835225\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> a) In this question, i is a unit vector due east and j is a unit vector due north. <BR>\n" );
document.write( " A cyclist rides at a speed of 4ms−1 on a bearing of 015°. Write the velocity vector of the cyclist in the form xi + yj, where x and y are constants.<BR>\n" );
document.write( "------<BR>\n" );
document.write( "x = 4*sin(15)<BR>\n" );
document.write( "y = 4*cos(15)<BR>\n" );
document.write( "===============<BR>\n" );
document.write( "(b) A vector of magnitude 6 on a bearing of 300° is added to a vector of magnitude 2 on a bearing of 230° to give a vector v. Find the magnitude and bearing of v.<BR>\n" );
document.write( "-----------<BR>\n" );
document.write( "Use the Cosine Law to find the magnitude of r, the resultant:<BR>\n" );
document.write( "r^2 = 6^2 + 2^2 - 1*6*2*cos(110)<BR>\n" );
document.write( "r =~ 6.6411<BR>\n" );
document.write( "---<BR>\n" );
document.write( "Use the Law of Sines to find the angle at the Origin:<BR>\n" );
document.write( "6.6411/sin(110) = 2/sin(A)<BR>\n" );
document.write( "sin(A) = 2*sin(110)/6.6411 = ~0.28299A = ~16.439 degs<BR>\n" );
document.write( "Bearing = A + 300 = 316.439 degs </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );