An airplane flies 80 km in a direction 50° east of north to a hub city, then 50 km in a direction 30° north of west, and then 30 km to the north to a final destination.what the magnitude and direction

Answer 1

We need to first find the angles in the unit circle

50 degrees east of north is 40 degrees

30 degrees north of west is 150 degrees

North is 90 degrees

The x components are 80 cos 40 + 50 cos 150 + 30 cos 90 = 18 km (East)

The y components are 80 sin 40 + 50 sin 150 + 30 sin 90 = 106.4 km (North)

The resultant is 107.9 km at an angle of 80.4 degrees

Answer 2

Each leg of the trip is broken down into North/South and East/West Components. The final resultant is determined by adding the relative components. Then a resultant angle and direction is determined.

Leg 1 - 80 km 50⁰ East of North North Component= 80 cos 50⁰ = 51.4 km East = 80 sin 50⁰ = 61.3 km E

Leg 2 - 50 km 30⁰ North of West North Component= 50 sin 30⁰ = 25 km West = 50 cos 30⁰ = 43.3 km W

Leg 3 - 30 km North

Total North Component = 51.4 + 25 + 30 = 106.4 km North

Total East Component = 61.3 - 43.3 = 18 km East

Resultant Distance² = 106.4² + 18² = 11,645; Resultant Distance = Sq Root 11,645 = 107.9 km

Bearing : tan^-1 106.4/18 = 80.4⁰ North of East