Question

Without the wind, a plane would fly due east at a rate of 150 mph. The wind is blowing southeast at a rate of 50 mph. The wind is blowing at a 45 angle from due east. What is the actual speed of the plane with the wind?

Answer 1

The actual speed of the plane with the wind:
v² = ( 150 + 50 · cos 45°)² + ( 50 · sin 45°)²
v² = ( 150 + 35.355 )² + 35.355²
v² = 34,356.467 + 1,249.976
v = √35,606.452
v = 188.7 mph