a jet airliner moving initially at 3.00 at 10^2mi/h due east enters a region whe

Question

a jet airliner moving initially at 3.00 at 10^2mi/h due east enters a region where the wind is blowing 1.00 x 10^2 mi/h in a direction 30 degrees north of east. A find the components of the velocity of the jet airliner relative to the air vector ja. b. find the components of the velocity of the air relative to earth vector ae. c. write the  equation analogous to equation for the velocities of vector ja, vector ae, and vector je. d. write the speed and direction of the aircraft relative to the ground?

Explanation / Answer

a) Relative to the air, the aircraft is doing 300mph. east. That doesn't change.
b) A wind of 100mph blowing 30 deg. N of E has components of (cos30 x 100) = 86.6mph east, and (sin30 x 100) = 50mph north.
c) For every hour it flies, the aircraft will be accelerated by 86.6mph, so 386.6 miles is the east component, and 50 miles is the north component. Speed over the ground is sqrt. (386.6^2 + 50^2) = 389.82mph.
The flight direction will be (50/389.82) = tan L, so atn = 7.3 deg.,N of E

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