document.write( "Question 1179989: Hi,\r
\n" ); document.write( "\n" ); document.write( "There's a word problem on vectors that I've been having trouble with: \"What direction and airspeed are required for a plane to fly 400 miles due north in 2.5 hours if the wind is blowing 11 mph in the direction of 58° east of north?\" I'm not sure where to start and how to draw a diagram to represent the problem and I'd love for some help on it!\r
\n" ); document.write( "\n" ); document.write( "Thank you! \n" ); document.write( "
Algebra.Com's Answer #809777 by htmentor(1343)\"\" \"About 
You can put this solution on YOUR website!
The resultant vector will have direction due north and magnitude equal to the
\n" ); document.write( "speed: 400 mi/2.5 h = 160 miles per hr
\n" ); document.write( "The air speed and heading of the plane must be able to counteract the speed
\n" ); document.write( "and direction of the wind. The direction of the wind is 58 deg E of N, which
\n" ); document.write( "is 32 deg N of E. The plane must head west of north to counteract this. Adding
\n" ); document.write( "the vectors head to tail, we get the resultant vector. The coordinates of the
\n" ); document.write( "end point of the resultant vector are given by (x,y) = (-11cos(32),160-11sin(32))
\n" ); document.write( "Thus the air speed is given by sqrt(x^2+y^2) = 154.45
\n" ); document.write( "The direction is given by atan(x/y) = -3.46 deg, or 3.46 deg W of N
\n" ); document.write( "Ans: speed = 154.45 mph, direction 3.46 deg W of N
\n" ); document.write( "See attached diagram.
\n" ); document.write( " \n" ); document.write( "
\n" );