document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1202456>Question 1202456</A>: <I><SPAN STYLE=\"word-break: break-all;\"> a car travels from point C northward for 1 hr then eastward for half an hour, then shifted N 30 E. if the constant speed of the car is 40kph, how far directly from point c will it be after 2 hrs. </SPAN>\n" );
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document.write( "Answer: <font color=red>64.6965 km (approximate)</font>\r<BR>\n" );
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document.write( "Explanation:\r<BR>\n" );
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document.write( "Draw an xy axis.<BR>\n" );
document.write( "Place point C at the origin.\r<BR>\n" );
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document.write( "The car drives north at 40 kph for 1 hour.<BR>\n" );
document.write( "Distance = rate*time<BR>\n" );
document.write( "Distance = (40 kph)*(1 hr)<BR>\n" );
document.write( "Distance = 40 km<BR>\n" );
document.write( "The car drives 40 km north for the first leg of the trip.<BR>\n" );
document.write( "Move from point C(0,0) to point A(0,40)\r<BR>\n" );
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document.write( "For the next leg of the trip, we have<BR>\n" );
document.write( "Distance = rate*time<BR>\n" );
document.write( "Distance = (40 kph)*(1/2 hr)<BR>\n" );
document.write( "Distance = 20 km<BR>\n" );
document.write( "This will move us from A(0,40) to B(20,40) when going 20 km east.\r<BR>\n" );
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document.write( "The notation N 30 E means \"face north, then turn 30 degrees eastward\". <BR>\n" );
document.write( "This is equivalent to the notation E 60 N where we face east and then turn 60 degrees toward the north.<BR>\n" );
document.write( "30+60 = 90<BR>\n" );
document.write( "See this page for more info about compass bearings.<BR>\n" );
document.write( "<a  rel=nofollow HREF= \"http://academic.brooklyn.cuny.edu/geology/leveson/core/linksa/comp.html\">http://academic.brooklyn.cuny.edu/geology/leveson/core/linksa/comp.html</a>\r<BR>\n" );
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document.write( "The notation E 60 N is more useful because 60 degrees is the reference angle. <BR>\n" );
document.write( "Use polar coordinates as an offset to move from B(20,40) to D(30,57.320508)\r<BR>\n" );
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document.write( "The scratch work to determine the x,y coordinates of D are shown in this paragraph<BR>\n" );
document.write( "r = distance traveled for the remaining 1/2 hr = 20 km<BR>\n" );
document.write( "theta = 60 degree reference angle<BR>\n" );
document.write( "(xB,yB) = x and y coordinates of point B<BR>\n" );
document.write( "x = xB + r*cos(theta)<BR>\n" );
document.write( "x = 20 + 20*cos(60)<BR>\n" );
document.write( "x = 30<BR>\n" );
document.write( "y = yB + r*sin(theta)<BR>\n" );
document.write( "y = 40 + 20*sin(60)<BR>\n" );
document.write( "y = 57.320508 which is approximate<BR>\n" );
document.write( "Make sure your calculator is in degree mode.\r<BR>\n" );
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document.write( "To recap the journey:<ul><li>Start at C(0,0)</li><li>Move 40 km north to arrive at A(0,40)</li><li>Move 20 km east to get to B(20,40)</li><li>Move 20 km along the compass bearing N 30 E (aka E 60 N) to arrive at the approximate location D(30,57.320508)</li></ul>The pathway is C to A to B to D in that exact order.\r<BR>\n" );
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document.write( "The question is: how far is it from the start point C(0,0) to the end point D(30,57.320508)?\r<BR>\n" );
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document.write( "We could draw a right triangle and use the pythagorean theorem.<BR>\n" );
document.write( "Or we could use the distance formula.\r<BR>\n" );
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document.write( "I'll use the distance formula.<BR>\n" );
document.write( "(x1,y1) = (0,0) and (x2,y2) = (30,57.320508)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d+=+sqrt%28+%28x1-x2%29%5E2+%2B+%28y1-y2%29%5E2+%29 ALIGN=MIDDLE  ALT=\"d+=+sqrt%28+%28x1-x2%29%5E2+%2B+%28y1-y2%29%5E2+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d+=+sqrt%28+%280-30%29%5E2+%2B+%280-57.320508%29%5E2+%29 ALIGN=MIDDLE  ALT=\"d+=+sqrt%28+%280-30%29%5E2+%2B+%280-57.320508%29%5E2+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d+=+sqrt%28+%28-30%29%5E2+%2B+%28-57.320508%29%5E2+%29 ALIGN=MIDDLE  ALT=\"d+=+sqrt%28+%28-30%29%5E2+%2B+%28-57.320508%29%5E2+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d+=+sqrt%28+900+%2B+3285.64063737806+%29 ALIGN=MIDDLE  ALT=\"d+=+sqrt%28+900+%2B+3285.64063737806+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d+=+64.6965272435706 ALIGN=MIDDLE  ALT=\"d+=+64.6965272435706\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "This is the approximate distance from C(0,0) to D(30,57.320508)<BR>\n" );
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