An airplane takes off at a ground velocity of 200km/hr toward the east, climbing at an angle of 14 degrees. A 20km/hr wind is blowing from the north. Determine the resultant air and ground velocities and their magnitudes.

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- Jun 1st 2009, 03:39 PMdalbir4444Finding resultants in 3-dimensions
An airplane takes off at a ground velocity of 200km/hr toward the east, climbing at an angle of 14 degrees. A 20km/hr wind is blowing from the north. Determine the resultant air and ground velocities and their magnitudes.

- Jun 1st 2009, 11:02 PMearboth
Use a coordinate system with the x-axis pointing East, the y-axis pointing North and the z-axis pointing up into the sky.

Then the North wind can be described by:

and the starting airplane as

The resulting vector which described the way of the airplane is:

and it's magnitude is:

The course over ground is described by:

which yields

- Jun 2nd 2009, 04:08 AMdalbir4444
The back of my book says that the air velocity is [200, 20, 200 tan14] which gives a magnitude of 207.1 km/h.

Also, the ground velocity is given as[200,20,0] which gives a magnitude of 201.0 km/h.

I couldn't make sense of this answer. Should I assume that the book is wrong. - Jun 2nd 2009, 06:09 AMearboth