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.
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.
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
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.