Precalculus Vector problem

Question

An airplane is heading due north at 260 mph (air speed). a 16 mph window blows from the northwest at an angle of 110 degrees clockwise from the north.Find the true speed (ground speed ) and direction of the plane.

Answer 1

If the wind is from 110 degrees clockwise from due north, then it is mostly from the EAST. You may need to re-check the wording of the problem.

Regardless, solve this kind of problem as follows:

1. Plot the vectors on graph paper to help visualize. Make the plot approximately to scale. Due north can be + y, and due east can be + x
2. Find the x and y components of each vector. For the airspeed, there is no x component and y(air) = 260. For the wind, y(wind) = 16 * sin(110), and x(wind) = 16 * cos(110)
3. Add up the x and y components:
4. x(total) = 16 * cos(11)
5. y(total) = 260 + 16 * sin(11)
6. Use trig or the Pythagorean Theorem to find the magnitude and direction of the new vector