The runway of an airfield faces west. An airplane, flying in the direction of north-east at a height of 2km and at a speed of 400km/h, on a path which passes over a point 3km west of the runway end, is spotted sqrt(29)km horizontally(south-western quadrant) from the runway end. At this tiem another airplane takes off from the airfield and climbs at an angle of 30degrees with a constant speed of 250km/h.
a) Find the trajectories of both airplanes
b) Determine whether the two planes are in danger of collision.
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