A plane is headed due west with an air speed of 300 mph. The wind is from the north at 80 mph. Find the bearing for the course and the ground speed of the plane.
ground speed = √(300^2+80^2) = 20√241 = 310.48 mph
bearing = arctan(-80/-300) = 255.1° = W14.9°S
steve, you are the man! i wish i had your brain.
hang in there. after you have done as many of these as I have, they'll be a cinch!
To find the bearing for the course and the ground speed of the plane, we can use vector addition.
1. Start by drawing a diagram to visualize the situation. Draw a straight line to represent the course of the plane (heading due west) and label it "Plane's course". Draw an arrow pointing directly west.
2. Next, draw an arrow pointing north to represent the wind, with a length of 80 units, and label it "Wind vector".
3. To find the ground speed, we need to add the vectors. In this case, we can visualize it as "subtracting" the wind vector from the course vector since the wind is opposing the plane's movement.
4. Start by drawing a line that is parallel to the wind vector, starting from the head of the wind vector and extending towards the west. This line represents the "correction vector" needed to cancel out the effect of the wind.
5. Measure the length of the correction vector. This length represents the ground speed of the plane. In this case, the ground speed is equal to the magnitude of the correction vector.
6. To find the bearing for the course, measure the angle between the correction vector and the original course vector using a protractor. This angle represents the bearing for the course.
By following these steps, you can visually determine the bearing for the course and the ground speed of the plane.