document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=106431>Question 106431</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0435510746/algebrahomeworkh>Mechanics I </A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> Hey again! :D Im stuck on this question about vectors including acceleration and relative positioning.\r<BR>\n" );
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document.write( "The question is..\r<BR>\n" );
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document.write( "A particle has position 2i + j initially and is moving with speed 10ms-1 in the direction 3i - 4j. Find it's position vector when t = 3 and the distance it has travelled in those 3 seconds.\r<BR>\n" );
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document.write( "I know the distance travelled is Speed * time, so 10 * 3 = 30metres. But when i worked out the relative position i got it totally wrong, does anyone know how to do this? Thanks alot in advance! :D </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #77436 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=77436\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A particle has position 2i + j initially and is moving with speed 10ms-1 in the direction 3i - 4j. Find it's position vector when t = 3 and the distance it has travelled in those 3 seconds. <BR>\n" );
document.write( "I know the distance travelled is Speed * time, so 10 * 3 = 30metres. <BR>\n" );
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document.write( "Draw the figure:<BR>\n" );
document.write( "A vector from (2,1) thru (3,-4) and extended to (x,y)<BR>\n" );
document.write( "A vertical segment from (2,1) down to (2,-4)<BR>\n" );
document.write( "A horizontal segment form (2,-4) to (3,-4)<BR>\n" );
document.write( "These form a triangle with hypotenuse = sqrt(26),<BR>\n" );
document.write( "vertical = 5, horizontal = 1.<BR>\n" );
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document.write( "Need to find x and y.<BR>\n" );
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document.write( "The diagonal distance is 30 meters as you pointed out.<BR>\n" );
document.write( "So x^2 + y^2 = 900<BR>\n" );
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document.write( "Draw a vertical line from (2,1) down to (2,y)<BR>\n" );
document.write( "Draw a horizontal line from (2,y) to (x,y)<BR>\n" );
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document.write( "You now have two proportional triangles.<BR>\n" );
document.write( "Vertical Proportion: 30/sqrt(26) = v/5<BR>\n" );
document.write( "v = 150/sqrt26 = 29.417 <BR>\n" );
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document.write( "Horizontal Proportion:<BR>\n" );
document.write( "30/sqrt(26)= h/1<BR>\n" );
document.write( "h = 5.88<BR>\n" );
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document.write( "Therefore:<BR>\n" );
document.write( "x = 2+h = 7.88<BR>\n" );
document.write( "y = 1-29.417 = -28.417<BR>\n" );
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document.write( "These are the position coordinates after 3 seconds.<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.\r<BR>\n" );
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