document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=803720>Question 803720</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A boats start To cross a river upstream at an angle of 140 deg to the flaw of the river the boat moves directly across the river at 10m/s as a result of combined effect of the velocity of the stream and the velocity of the boat. Calculate<BR>\n" );
document.write( "(a) the velocity of the stream.<BR>\n" );
document.write( "(b)the velocity of the boat in still in water. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #484462 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39618)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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=484462\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> You may be able to draw this picture:\r<BR>\n" );
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document.write( "Horizontal axis, current of river toward the right; vertical axis, upward is \"accross\" the river straight up.\r<BR>\n" );
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document.write( "The boat is trying to go into quadrant 4, so that direction of the boat vector is 140 degrees, using  \"to the right...\" as the reference direction, the positive x axis.  The river vector is just toward the right, no angle, since angle 0 is unrotated and toward the right.\r<BR>\n" );
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document.write( "b for the boat's magnitude, r for the river's magnitude.<BR>\n" );
document.write( "The boat vector is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%2Acos%28140%29%2Bb%2Asin%28140%29 ALIGN=MIDDLE  ALT=\"b%2Acos%28140%29%2Bb%2Asin%28140%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The river vector is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%2Acos%280%29%2Br%2Asin%280%29 ALIGN=MIDDLE  ALT=\"r%2Acos%280%29%2Br%2Asin%280%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The sum of the vectors for b and r is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10%2A%28cos%2890%29%2Bsin%2890%29%29 ALIGN=MIDDLE  ALT=\"10%2A%28cos%2890%29%2Bsin%2890%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Adding the components will give you two equations.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%2Acos%28140%29%2Br%2Acos%280%29=10%2Acos%2890%29 ALIGN=MIDDLE  ALT=\"b%2Acos%28140%29%2Br%2Acos%280%29=10%2Acos%2890%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >  and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%2Asin%28140%29%2Br%2Asin%280%29=10%2Asin%2890%29 ALIGN=MIDDLE  ALT=\"b%2Asin%28140%29%2Br%2Asin%280%29=10%2Asin%2890%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%28-0.766%29%2Br=10%2A0 ALIGN=MIDDLE  ALT=\"b%28-0.766%29%2Br=10%2A0\"   DISABLED_style= \"max-width:90%; height:auto;\" >  and  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%2A%280.643%29%2Br%2A0=10%2A1 ALIGN=MIDDLE  ALT=\"b%2A%280.643%29%2Br%2A0=10%2A1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-0.766b%2Br=0 ALIGN=MIDDLE  ALT=\"-0.766b%2Br=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.643b=10 ALIGN=MIDDLE  ALT=\"0.643b=10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "'<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=0.766b ALIGN=MIDDLE  ALT=\"r=0.766b\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=10%2F%280.643%29 ALIGN=MIDDLE  ALT=\"b=10%2F%280.643%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Second part simplified is then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28b=15.55%29 ALIGN=MIDDLE  ALT=\"highlight%28b=15.55%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and therefore <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=0.766%2A15.55=highlight%2811.91%29 ALIGN=MIDDLE  ALT=\"r=0.766%2A15.55=highlight%2811.91%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "If you prefer for proper accuracy, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=16 ALIGN=MIDDLE  ALT=\"b=16\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=12 ALIGN=MIDDLE  ALT=\"r=12\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
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