An aircraft is travelling at 30 degrees to the horizontal, a crosswind is blowing due east at 70km/h, whereas the aircraft is travelling at 500km/h

Question

B) Use the cosine rule to determine the resultant speed and deflection of the aircraft.

C) Describe the course correction that the pilot must make to arrive on course.

Answer 1

plane going 30 degrees (pi/6) to the horizontal at 500 kph

wind blows east at 70 kph

what is the plane's direction and speed??

construct a parallelogram with adjoining sides 70 and 500

with 30 degree angle between them

calculate the diagonal to find speed, d, d^2 = 70^2 +500^2 -2(70)(500)cos30

= 4900 + 250,000 - 70000(sqr3)/2 = 254,900 - 35,000sqr3

d = sqr(254,900 - 35,000sqr3 = about 440.77 kph

sinB/500 = sin30/440.77 = (1/2)/440.77

sinB= 250/440.77= about .5672

B = arcsin.5672= 34.56 degrees = plane's angle with the horizon but it should be <30

so try

sinB/70 = sin30/440.77

sinB = 35/440.77

B = arcsin(35/440.77) = about 4.55 degrees. <30 so it may be right