Find the true course/ heading in degrees.

Question

Use your knowledge of bearing, heading, and true course to sketch a diagram that will help you solve the problem.

A plane is flying with an airspeed of 170 miles per hour and heading 135°. The wind currents are running at 30 miles per hour at 175° clockwise from due north. Use vectors to find the true course and ground speed of the plane. (Round your answers to the nearest ten for the speed and to the nearest whole number for the angle.)

Answer 1

The air speed can be divided into 2 components: 170 mph (sin 135°) = 120 mph to the east and 170 mph (cos 135°) = -120 mph to the north (or more simply 120 mph south).

The wind speed components are 30 mph (sin 175°) = 2.6 mph to the east and 30 mph (cos 175°) = -29.9 mph to the north (or more simply 29.9 mph south)

Adding the vectors produces the ground speed:

v_easterly = 123 mph ; v_southerly = 150 mph

The angle (southerly relative to due east) is tan^-1(150/123) ≈ 51°, so the heading is 141°. The magnitude of the ground speed is 150 mph/sin 51° = 190 mph