document.write( "Question 114732: An airplane is flying at 340 mph with a heading of 210 degrees. If a 50 mph wind is blowing from the west, find the actual ground speed and course of the airplane. \n" ); document.write( "

Algebra.Com's Answer #83531 by Fombitz(32388) $\"\"$ $\"About$

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Assuming east is positive x, north is positive y, break down the airplane's velocity into a vector in the x-y plane.
\n" ); document.write( "The plane is traveling 340 mph at a bearing of 210 degrees or (340cos(210), 340 sin(210)).
\n" ); document.write( "The wind is blowing from the west (to the east) at 50 mph or (50,0).
\n" ); document.write( "The actual ground speed would be the vector sum of those two (340 cos(210)+50, 340 sin(210)) or (-294.4+50,-170) or (-244.4,-170).
\n" ); document.write( "The magnitude of that velocity vector is
\n" ); document.write( " $\"V%5E2=244.4%5E2%2B170%5E2\"$
\n" ); document.write( " $\"V%5E2=88655\"$
\n" ); document.write( " $\"V=297.8\"$
\n" ); document.write( "For direction
\n" ); document.write( " $\"tan%28alpha%29+=+170%2F244.4\"$
\n" ); document.write( " $\"tan%28alpha%29+=+0.6956\"$
\n" ); document.write( " $\"%28alpha%29+=+34.8\"$
\n" ); document.write( "Since this angle is measured from the (-y) axis, we add 180 to get the actual heading.
\n" ); document.write( "The plane is traveling at 297.8 mph at a heading of 214.8 degrees. \n" ); document.write( "

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