A plane is flying due south at a speed of 192 mph. a wind is blowing in at 53 degrees at 13 mph. what is the bearing of the plane?
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 ?
Assuming the normal 0° at North, and ignoring the misuse of the word "bearing", I'd say that the resultant heading of the plane is 246.7°
I meant 336.7°
To find the bearing of the plane, we need to consider the combination of the plane's true heading and the wind's direction.
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.