Question

03.3 You fly an airplane to a city that is 800 miles to the west and 300 miles to the north of your starting point. The wind is blowing from east to west. Your plane has an airspeed of 200 mph and the trip takes 3.55 hours. a) In what direction did you aim the plane? b) What is the speed of the wind?

Answer 1

(a) where R be resultant R = squareroot (800)^2 + (300)^2 R = 854.4 miles and the direction of R is tan theta = 300/800 = 0.375 theta = tan^-1 (0.375) theta = 20.55 degree we have to aim the plane in the direction which makes an angle theta = 20.55 degree from west to north (b) let v be the wind speed plane speed is v_p = 200 m p h The wind is blowing from east to west then components of wind speed along the plane direction is = v cos theta = v cos (20.55) total speed = v_p + v cos (20.55) Now we use the formula distance = speed times time R = (v_p + v cos (20.55)) times t 854.4 = (200 + v times 0.936) times 3.55 v times 0.936 = 40.67 v = 43.45 m p h This is the speed of the wind