You are traveling on an airplane. The velocity of the plane with respect to the air is 160 m/s due east. The velocity of the air with respect to the ground is 41 m/s at an angle of 30° west of due north.

1)

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the velocity of the air is

41*sin30=20.5 m/s to west

41*cos30 = 35.5 m/s to north

the velocity of the plane to the ground is thus

160-20.5 = 139.5 m/s to east and 35.5 m/s to the south

the speed is sqrt(139.5^2+35.5^2) = 143.9 m/s

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