document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=998492>Question 998492</A>: <I><SPAN STYLE=\"word-break: break-all;\"> To a person riding a bike with velocity (7 i + 3 j) km/h the wind seems to have velocity (9 i + 10 j) km/h. \r<BR>\n" );
document.write( "\n" );
document.write( "State the true velocity of the wind in i, j vector form.<BR>\n" );
document.write( "velocity (km/h) = \r<BR>\n" );
document.write( "\n" );
document.write( "What is the speed of the wind?<BR>\n" );
document.write( "speed (km/h) = \r<BR>\n" );
document.write( "\n" );
document.write( "Taking i as due East, what is the direction of the wind (in standard bearing notation) to the nearest degree?<BR>\n" );
document.write( "bearing (°) &#8776;\r<BR>\n" );
document.write( "\n" );
document.write( "THANK YOU </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #616417 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52781)</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=616417\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
document.write( "To a person riding a bike with velocity (7 i + 3 j) km/h the wind seems to have velocity (9 i + 10 j) km/h. <BR>\n" );
document.write( "State the true velocity of the wind in i, j vector form.<BR>\n" );
document.write( "velocity (km/h) = <BR>\n" );
document.write( "What is the speed of the wind?<BR>\n" );
document.write( "speed (km/h) = <BR>\n" );
document.write( "Taking i as due East, what is the direction of the wind (in standard bearing notation) to the nearest degree?<BR>\n" );
document.write( "bearing (°) &#8776; <BR>\n" );
document.write( "-------------------------------------------------------------------------\r<BR>\n" );
document.write( "\n" );
document.write( "To a person riding a bike with velocity &nbsp;(r*i + s*j) &nbsp;<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=km%2Fh ALIGN=MIDDLE  ALT=\"km%2Fh\"   DISABLED_style= \"max-width:90%; height:auto;\" >&nbsp; in a &nbsp;<U>still air</U>&nbsp; (at no wind) &nbsp;the wind &nbsp;<U>seems</U> &nbsp;to have velocity &nbsp;(-r*i, -s*j) &nbsp;<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=km%2Fh ALIGN=MIDDLE  ALT=\"km%2Fh\"   DISABLED_style= \"max-width:90%; height:auto;\" >. &nbsp;From here I make a conclusion that \r<BR>\n" );
document.write( "\n" );
document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- if a person is riding a bike with velocity &nbsp;(r*i + s*j)&nbsp; <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=km%2Fh ALIGN=MIDDLE  ALT=\"km%2Fh\"   DISABLED_style= \"max-width:90%; height:auto;\" > &nbsp;relative to the earth surface and \r<BR>\n" );
document.write( "\n" );
document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- if the wind is &nbsp;(u*i + v*j)&nbsp; <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=km%2Fh ALIGN=MIDDLE  ALT=\"km%2Fh\"   DISABLED_style= \"max-width:90%; height:auto;\" > &nbsp;relative to the earth surface, \r<BR>\n" );
document.write( "\n" );
document.write( "then for the person the wind seems to have velocity &nbsp;((u-r)*i, (v-s)*j).\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Thus we have the equations for the unknowns wind's velocity components (u*i, v*j)\r<BR>\n" );
document.write( "\n" );
document.write( "u - 7 = 9 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;(for i-direction), &nbsp;&nbsp;and \r<BR>\n" );
document.write( "\n" );
document.write( "v - 3 = 10 &nbsp;&nbsp;&nbsp;&nbsp;(for j-direction).\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "It gives for the wind's velocity components &nbsp;&nbsp;u = 7+9 = 16 <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=km%2Fh ALIGN=MIDDLE  ALT=\"km%2Fh\"   DISABLED_style= \"max-width:90%; height:auto;\" > &nbsp;for i-direction, &nbsp;&nbsp;and &nbsp;&nbsp;v = 3+10 = 13 <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=km%2Fh ALIGN=MIDDLE  ALT=\"km%2Fh\"   DISABLED_style= \"max-width:90%; height:auto;\" > &nbsp;for j-direction.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Hence. &nbsp;the speed of the wind is &nbsp;&nbsp;<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2816%5E2+%2B+13%5E2%29 ALIGN=MIDDLE  ALT=\"sqrt%2816%5E2+%2B+13%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28425%29 ALIGN=MIDDLE  ALT=\"sqrt%28425%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 20.6 <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=km%2Fh ALIGN=MIDDLE  ALT=\"km%2Fh\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );