document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=21312>Question 21312</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Okay i need to know how to solve this question, The U.S.S. Independence maintains a constant speed of 10 knots heading due north. At 4:00 pm the ship's radar detects a destroyer 100 nautical miles due east of the carrier. If the destroyer is heading due west at 20 knots, when will the two ships be the closet? (1 knot= 1 nautical mile) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #10298 by </B><A HREF=/tutors/aboutme.mpl?userid=Photonjohn><B>Photonjohn(42)</B></A><img src=\"/images/stars/stars-07.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Photonjohn><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=10298\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> You have a right triangle with northern leg of 10T or 10 knots for a time T.<BR>\n" );
document.write( "You have the right leg of 100 miles minus 20 knots for a time T<BR>\n" );
document.write( "So the distance between them is the hypotenuse which is the square of the sum of these two legs.\r<BR>\n" );
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document.write( "Distance D^2 = ((10T)^2 + (100-20T)^2<BR>\n" );
document.write( "D = ( 100T^2 + (100-20T)^2)^1/2<BR>\n" );
document.write( "differentiate this distance with respect to time T<BR>\n" );
document.write( "dD/dT = d/DT( of the above)<BR>\n" );
document.write( "set = to 0<BR>\n" );
document.write( "let u = (...) above<BR>\n" );
document.write( "0 = d/DT ( u )1/2 letting u = simplifed (...) = 500(T^2 - 8T + 20)<BR>\n" );
document.write( "du/DT = 500(2T - 8)<BR>\n" );
document.write( "yields <BR>\n" );
document.write( "0 = 2T - 8<BR>\n" );
document.write( "T = 4 hours<BR>\n" );
document.write( "At 4 hours, the carrier is 40 nmiles north and the destroyer has moved 100 - 80 nmiles west.  The distance is the square root of 40^2 + 20^2 or (2000)^1/2 = 44.7 miles apart.\r<BR>\n" );
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document.write( "checking out a time greater than 4 hours, say 5 hours, yields legs of 50 miles north and (100-100) east = square root of 2500 = 50 miles apart.\r<BR>\n" );
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document.write( "checking our a time less than 4 hours, say 3 hours, yields legs of 30 miles north and (100-60) = 40 miles east = square root of 2500 = 50 miles apart.\r<BR>\n" );
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document.write( "This shows a minimum at T = 4 hours which is 44.7 k miles apart.\r<BR>\n" );
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document.write( "If you have a graphing calculator, you can see the graph reach the minimum at 44.7 k miles.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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