An airplane is heading due south at a speed of 632 kmh A wi

An airplane is heading due south at a speed of 632 km/h . A wind begins blowing from the southwest at a speed of 70 km/h (average). In what direction should the pilot aim the plane so that it will fly due south? Express your answer to three significant figures and include the appropriate units. TRIED IT LIKE 10 DIFFERENT WAYS DON\'T KNOW WHAT I\'M DOING WRONG PLEASE EXPLAIN EACH STEP

Solution

v_{plane rela ground} = v_{plane rela air} + v_{plane rela ground}

= (0, -632) + (70 cos 45, 70 sin 45)

= (49.49, -582.51)

u = sqrt [49.49² + 582.51²] = 585 km/h

theta = tan-1 [49.49 / 582.51]

= 4.85 deg east of south