You are traveling on an airplane. The velocity of the plane with respect to the

Question

You are traveling on an airplane. The velocity of the plane with respect to the air is 190.0 m/s due east. The velocity of the air with respect to the ground is 33.0 m/s at an angle of 30

Explanation / Answer

Airplane is moving at 190m/s wrt to air in south due west and air is moving at 33m/s wrt ground in north direction. Now if we consider +x axis(i) as East ;-x axis(-i) as west ;+y axis(j) as North; -y axis(-j) as South, we can resolve the vector components of velocity. (a)Now velocity airplane wrt air=190sin(30)(-j)+190cos(30)(-i)=-95j-164.544i Velocity of air wrt ground is 33j therefore velocity of Airplane wrt ground =-95j-164.544i+33j=-62j-164.5i ==> speed of plane wrt ground is 175.79m/s (b) I have written the vectors for airplane velocity wrt ground -62j-164.5i you can nw resolve it in degree r anyway you like (c)How far west will the plane travel in 1 hour: Velocity component of plane in west direction is -62j, therefore plane will travel 62 km in West direction in 1hr. I hope this helped.Please Rate

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