document.write( "Question 318803: An airplane has an airspeed of 510 km/h bearing 50 deg north of east. The wind is 70 km/h in the direction 33 deg north of west. Find the resultant velocity representing the path of the airplane with resprect to the ground. \n" ); document.write( "
Algebra.Com's Answer #228213 by CharlesG2(834)\"\" \"About 
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An airplane has an airspeed of 510 km/h bearing 50 deg north of east. The wind is 70 km/h in the direction 33 deg north of west. Find the resultant velocity representing the path of the airplane with resprect to the ground.\r
\n" ); document.write( "\n" ); document.write( "call North 0 degrees, East 90, South 180, West 270
\n" ); document.write( "50 deg north of east = 90 - 50 = 40 degreesA
\n" ); document.write( "33 deg north of west = 270 + 33 = 303 degrees
\n" ); document.write( "airplane 510 km/h at 40 degrees (call this Vector A)
\n" ); document.write( " wind 70 km/h at 303 degrees (call this Vector W)
\n" ); document.write( "okay these are vectors, vectors have a horizontal component and a vertical component and a magnitude
\n" ); document.write( "x = horizontal component = hypotenuse * cos(theta)
\n" ); document.write( "theta is the heading, the magnitude is the hypotenuse
\n" ); document.write( "y = vertical component = hypotenuse * sin(theta)
\n" ); document.write( "magnitude = sqrt(x^2 + y^2)
\n" ); document.write( "Vector A = 510 km/h at 40 degrees
\n" ); document.write( "Vector W = 70 km/h at 303 degrees
\n" ); document.write( "Ax = 510cos(40), Ay = 510sin(40)
\n" ); document.write( "Wx = 70cos(303), Wy = 70sin(303)
\n" ); document.write( "resultant vector horizontal component = Ax + Wx
\n" ); document.write( "Ax + Wx = 510cos(40) + 70cos(303) = 88.92478
\n" ); document.write( "resultant vector vertical component = Ay + Wy
\n" ); document.write( "Ay + Wy = 510sin(40) + 70sin(303)
\n" ); document.write( "Ay + Wy = -497.06
\n" ); document.write( "magnitude resultant vector = sqrt(88.92478^2 + (-497.06)^2)
\n" ); document.write( "magnitude resultant vector = 504.9521 km/h
\n" ); document.write( "direction resultant vector:
\n" ); document.write( "arctan of resultant vector = (Ay + Wy)/(Ax + Wx)
\n" ); document.write( "(Ay + Wy)/(Ax + Wx) = -497.06/88.92478 = -5.58967
\n" ); document.write( "arctan(-5.58967) = -79.857 degrees -->
\n" ); document.write( "360 - 79.857 = 280.143 degrees
\n" ); document.write( "the resultant velocity representing the path of the airplane with resprect to the ground is 504.95 km/h at 280.14 degrees (10.14 degrees north of west)
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