Find the mi/hr with 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 wind is 40° clockwise of the plane direction. Thus, the angle is 140°. Then, the ground speed is√

√(170²+30²-2*170*30*cos 40°) = 193.942396911592.

Let B be the angle of the ground heading from the air heading. This will be opposite the wind speed length.

Then, sin 140°/193.942396911592 = sin B/30

B = sin-1 30 sin 140°/193.942396911592) = 5.70632922699308°

Then, the direction is 135° + 5.70632922699308° = 140.70632922699308°

Then, we round this to 190 mph at 141°.