An airplane is flying on a compass heading(bearing) of 340 degrees art 325 mph. A wind is blowing with the bearing 320 degrees at 40 mph, how do you find the component form of the velocity of the airplane?
1 Answer
Below are the formulas for X- and Y-components of the resulting movement as well as the amplitude and angle of this movement (all angles are measured according to trigonometric standard).
Explanation:
In navigation the angle of the course (on a compass) is counted clockwise from the North (so, the direction to the North is
The North on most maps is a vertically up direction.
In coordinate Geometry and Trigonometry, which we will use, angles are measured counterclockwise from the positive direction of the horizontal X-axis (the East on most maps).
Let's make a simple transformation into Trigonometric standard using the direction to the East as an X-axis.:
This is a problem on addition of two vectors. Each is defined by its amplitude and angle of direction:
airplane (vector
wind (vector
To add these two vectors, we represent both as sums of X-component and Y-component:
Both X-components act along the same direction, both Y-components act along the same direction. So, we can add X-components to get an X-component of the resulting movement and add Y-components to get a Y-component of the resulting movement.
Knowing two components of the resulting vector of movement, we can easily determine the amplitude
We leave the calculations to the person who suggested the problem.
If it's necessary to express the angle
(if the result is greater than