An airplane takes off traveling due east at 250 miles per hour relative to the ground. (a)The plane encounters a horizontal cross wind blowing 25◦ north of west at 40 miles per hour. Find the resultant speed of the plane relative to the ground. Round your answer to the nearest one hundredth. Make sure to include a diagram that demonstrates how you set up any relevant vectors.   b) Upon encountering a horizontal cross wind, the resultant velocity of the plane relative to the ground is given by〈270,−34.641〉 . Find the speed and direction of the cross wind. (State your direction in terms of the cardinal directions: north, south, east, west. Round your answer to the nearest hundredth.) Make sure to include a diagram that demonstrates how you set up any relevant vectors.

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