document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=890887>Question 890887</A>: <I><SPAN STYLE=\"word-break: break-all;\"> An aircraft flies downwind from A to B with speed of 400mph for 2 hours and returns in absence of wind in 2.5 hours. What is the wind speed?<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #773059 by </B><A HREF=/tutors/aboutme.mpl?userid=gargaditya><B>gargaditya(1)</B></A><img src=\"/images/stars/iconNewId_16x16.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=gargaditya><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=gargaditya><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=773059\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> There are 2 approaches to solve the same.\r<BR>\n" );
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document.write( "Ok after a lot of reading online I could not get a single page to highlight these points clearly:\r<BR>\n" );
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document.write( "1.When question says downwind or upwind it refers to Net or Vag(velocity of aeroplane with respect to ground)\r<BR>\n" );
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document.write( "2.Vaw(Velocity of plane with respect to air) aka speed in still air←-YES they mean same thing (still air means assuming air to be stationary and hence its velocity of plane relative to air):\r<BR>\n" );
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document.write( "this is a fixed value ie only groundspeed(Vag)aka net value of speed in a direction and windpeed keep changing as per condition/windspeed may add or subtract\r<BR>\n" );
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document.write( "3.distance calculations always use ‘net speed’ aka ‘groundspeed’\r<BR>\n" );
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document.write( "D=Snet *time\r<BR>\n" );
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document.write( "OR\r<BR>\n" );
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document.write( "D=Vag *time\r<BR>\n" );
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document.write( "——————-\r<BR>\n" );
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document.write( "Approach 1 :\r<BR>\n" );
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document.write( "Let speed of plane in still air be a (ie Vaw)\r<BR>\n" );
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document.write( "Let speed of wind be w\r<BR>\n" );
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document.write( "given, “NET” aka groundspeed(Vag)= a+w=400\r<BR>\n" );
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document.write( "Remember D=Snet X T\r<BR>\n" );
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document.write( "therefore distance =net speed Xtime = 400X 2 =800 mi\r<BR>\n" );
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document.write( "Returning back implies distance is same=800 mi\r<BR>\n" );
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document.write( "D=S’ XT’\r<BR>\n" );
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document.write( "using no wind condns ie net speed =a\r<BR>\n" );
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document.write( "800 =a X2.5\r<BR>\n" );
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document.write( "giving a=320\r<BR>\n" );
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document.write( "hence a+w=400 implies w=80\r<BR>\n" );
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document.write( "Approach 2:\r<BR>\n" );
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document.write( "According to relative velocity concept,\r<BR>\n" );
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document.write( "Vaw =Vag - Vwg (1)\r<BR>\n" );
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document.write( "(P.S. Here qty on left side signifies wind is the frame of reference AND also note that these are vectors ie take care of sign)\r<BR>\n" );
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document.write( "given 400mph is the GROUNDSPEED(OR NET)\r<BR>\n" );
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document.write( "**let speed of wind be w\r<BR>\n" );
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document.write( "ie Vaw= 400-(w) =400-w (2) (downwind means sign of w is positive like Vag and Vaw)\r<BR>\n" );
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document.write( "D=”Vag”*time =400*2=800 (3)\r<BR>\n" );
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document.write( "In second scenario,\r<BR>\n" );
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document.write( "Vaw= V’ag -V’wg **Always note Vaw remains same as first scenario,only vel of plane wrt ground and windspeed change\r<BR>\n" );
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document.write( "ie Vaw =V’ag -0 (4)\r<BR>\n" );
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document.write( "distance to go=distance to return back\r<BR>\n" );
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document.write( "and distance=V’agXtime‘ (5)\r<BR>\n" );
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document.write( "800= V’ a,g X t’\r<BR>\n" );
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document.write( "800=V’agX2.5 giving V’ag=320\r<BR>\n" );
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document.write( "therefore using eq 4,Vaw =V’ag=320 (6)\r<BR>\n" );
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document.write( "using eq 6 and eq 2\r<BR>\n" );
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document.write( "320=400-w\r<BR>\n" );
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document.write( "w=80 </SPAN>\n" );
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