A plane moves horizontally at 80m/s of it wants to fly due south and the wind is blowing 3m/s south west what course should he steer
To determine the course the plane should steer, we need to find the resultant velocity vector by combining the velocity of the plane with the velocity of the wind. Here's how we can calculate it:
1. Draw a diagram representing the velocities:
- Draw an arrow pointing to the right to represent the velocity of the plane (80 m/s).
- Draw an arrow pointing southwest to represent the velocity of the wind (3 m/s).
2. Break down the velocity of the wind into its components:
- The wind is blowing to the south and southwest, so we need to determine the southward (y-component) and westward (x-component) velocities.
- The southward component can be calculated by multiplying the magnitude of the wind speed (3 m/s) by the sine of the angle formed between the wind direction and the south direction (assuming a right angle triangle).
- The westward component can be calculated by multiplying the magnitude of the wind speed (3 m/s) by the cosine of the angle formed between the wind direction and the south direction.
3. Calculate the x-component and y-component of the resultant velocity:
- Since the plane is moving horizontally due south, the y-component of the resultant velocity will be the sum of the plane velocity and the southward component of the wind velocity.
- The x-component of the resultant velocity will be the sum of the westward component of the wind velocity.
4. Determine the magnitude and direction of the resultant velocity:
- The magnitude of the resultant velocity can be calculated using the Pythagorean theorem: Magnitude = sqrt(x-component^2 + y-component^2).
- The direction can be determined by finding the angle relative to the south direction using the inverse tangent function (tan^-1(y-component / x-component)).
Following these steps, you should be able to find the magnitude and direction of the resultant velocity.