A plane moves due east (directly toward the east) while the pilot of the plane p

Question

A plane moves due east (directly toward the east) while the pilot of the plane points the plane somewhat south of east, toward a steady wind that blows northeast. The velocity of the plane in still air is 350km/h while the wind speed is 80 km/h in the direction of 40 degree east of north. Determine the airspeed (relative to the ground) of the plane flying in the "cross wind" and the angle (relative to the easterly direction) that the pilot must maintain to sustain an easterly direction. Determine the amount of time that the plane will be delayed or arrive early due to the wind if it has to travel 600 km.

Explanation / Answer

The velocity of the plane with respect to wind Vpw = 350 km/h The velocity of wind with respect to ground Vwg = 80 km/h The velocity of plane with respect to ground Vpg From relative velocities          Vpg = Vpw + Vwg Resolve the vectors into components and solve along the axis by axis     alon y-axis            0 = - (350 km/h) sin + (80 km/h) sin400                   sin = (80/350) sin40 = 0.1469 then angle = 8.44 deg Now along x-axis                           Vpg = (350 km/h) cos8.440 + (80 km/h) cos400                          = 407.5 km/h The time taken in still air   t1 = 600 km / 350 km/h                                                = 1.71 h The time taken due to wind t2 = 600 km/407.5 km/h                                                = 1.47 h Therefore it will arrive earlier due to wind.                    

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