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The air is moving with a speed 41 m/s an angle of 30° west of due north. Airplane is moving with a speed 160 m/s with respect to air due east.
(a) speed of Airplane with respect to the ground :
Since the wind is having a speed of 41 m/s , it will move the air plane toward North as far as the earth is concerned . Hence we add the speed with the plane’s speed and find the resultant of these two speeds.
Since they are perpendicular to each other, the resultant is
√ (160 ^2 + 41^2) = 165.169 m/s and the direction is given by tan θ = northern velocity / Eastern velocity so that θ is the angle measured from North to west.
tan θ = 41 / 160 and θ = 14.373° east of north .
hence the speed of airplane is 165.17 m/s at angle 14.373° east of north viewed from the ground.
The speed of the plane in the west direction is 165.17 cos 14.373° = 160.20 m/s
we know the speed of the air plane with respect to the ground , and with respect to air will be the same since the wind is flowing perpendicular the planes’ speed .
hence Distance traveled in one hour = 160.20* 3600 =576708.7 m or 576.71km
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