An airplane has an airspeed of 430 miles per hour at a beari

An airplane has an airspeed of 430 miles per hour at a bearing of 135 degree. The wind velocity is 35 miles per hour in the direction of N 30 degree E. Find the resultant speed and direction of the airplane.

Solution

Assuming airplane is at bearing of 30 deg towards north.

wind is towards east

Vn = (724 kph)sin(30) = 724(1/2) = 362 kph

The airplane\'s velocity in the East direction :

Ve = (724 kph)cos(30) = 724(sqrt(3)/2) = 627 km/hr

Add to Eastern velocity the wind speed of 32 km/hr

Ve = 627 + 32 = 659 km/hr

The resultant velocity is:

Vr = sqrt(362² + 659²) = 752 kph

Direction is:

= tan^-1(362/659) = 28.78°