What is the resultant velocity of the plane?

A plane travels at 120 mph in still air. It is headed due south in a wind of 30 mph from the northeast. What is the resultant velocity of the plane? Find the magnitude and the drift angle. The drift angle is the angle between the intended line of flight and the true line of flight.|||Speed in North-south direction= 120 + 30 sin 45


Speed = 141.213 mph (Southerly)





Speed in East-West direction = 30 cos 45


Speed = 21.213 mph (Westerly)





Magnitude of total speed:


V^2 = 141.213^2 + 21.213^2


V = 142.797 mph





Drift angle:


tan A = (21.213 / 141.213)


A = arctan(21.213 / 141.213)


A = 8.543* to the West|||If you draw a line going north to south and mark that 120 and from the southernmost point another line going towards the south west and label that 30 you will have a velocity diagram. If you make the 120 and 30 to the same scale and you draw the angle accurately then you can simply read off the length from start to finish and the angle of drift.





If you want to calculate the velocity use the cosine rule. a^2 = b^2 + c^2 - 2bc cos(A)


a^2 = 120^2 + 30^2 - 2 * 120 * 30 * cos (135) = 20391


a = 142.8 mph





Then you use the sine rule to work out the drift angle. a/sinA = b/sinB = c/sinC


142.8/sin(135) = 30/sin(drift angle)





sin(driftangle) = 0.1485


drift angle = 8.54 degrees East of South