Not sure what notation you are using when you say
"blowing in at 53° "
is North your 0° and you are going clockwise, or
is 0° your positive x - axis and you are going counterclockwise ?
"blowing in at 53° "
is North your 0° and you are going clockwise, or
is 0° your positive x - axis and you are going counterclockwise ?
Here's how we can solve it step by step:
1. Draw a diagram: Draw a reference line representing the north direction. Mark a point on the line to represent the plane's position. Label this point as "P."
2. Determine the plane's heading: Since the plane is flying due south, its heading is 180 degrees.
3. Determine the wind's direction: The wind is blowing at an angle of 53 degrees with respect to the north direction.
4. Calculate the angle between the plane's heading and the wind's direction:
- To do this, subtract the wind's direction from the plane's heading: 180 degrees - 53 degrees = 127 degrees.
- The result, 127 degrees, is the angle between the plane's heading and the wind's direction.
5. Calculate the wind's effect on the plane's bearing:
- Use the law of sines to calculate the component of the wind acting in the direction opposite to the plane's heading.
- The formula is: (Wind speed) * sin(Angle) = Component of wind opposite to the plane's heading.
- Substitute the values into the formula: (13 mph) * sin(127 degrees) = -11.98 mph.
- The negative sign indicates that the wind is acting against the plane's heading direction.
6. Determine the bearing of the plane:
- Add the component of the wind acting against the plane's heading to the plane's heading: 180 degrees + (-11.98 mph).
- The result is approximately 168.02 degrees.
- Therefore, the bearing of the plane is approximately 168.02 degrees, almost due south.
Remember that bearings are usually measured clockwise from the north direction.