Help Needed: Vectors - Calculate Plane Velocity & Direction

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In summary, the conversation discusses the velocity of a plane in still air and the effect of wind on its movement. The plane has a speed of 40kmh-1 and is traveling in a direction of 65 degrees bearing. However, there is a wind blowing at a speed of 20kmh-1 from the south east. To express the velocity of the plane and wind in component form, the bearing of 65 degrees is converted to 25 degrees counter-clockwise from due East and the wind direction of 135 degrees counter-clockwise from East. The air vector is calculated as 40kmh-1 multiplied by the cosine and sine of 25 degrees and the wind vector is calculated as 20kmh-1
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Please can anyone help with:

a plane has speed in still air (no wind) of 40kmh-1 and is traveling in a direction of 65 degrees bearing but there is a wind blowing at a speed of 20kmh-1 from the south east. If I is east and J is north, express the velocity p for the plane in no wind and velocity w of the wind in component form.

Then calculate the resultant velocity and magnitude and direction??
 
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a plane has speed in still air (no wind) of 40kmh-1 and is traveling in a direction of 65 degrees bearing but there is a wind blowing at a speed of 20kmh-1 from the south east. If I is east and J is north, express the velocity p for the plane in no wind and velocity w of the wind in component form.

bearing of 65 degrees is measured clockwise from due North = 25 degrees CCW from due East

wind from SE blows toward 135 degrees CCW from East

Air vector ...

$\vec{A}= 40\cos(25)\vec{i}+40\sin(25)\vec{j}$

Wind vector ...

$\vec{W} = 20\cos(135) \vec{i} + 20\sin(135)\vec{j}$Air vector + Wind vector = Track (resultant) vector

can you finish?
 

1. What is a vector and why is it important in calculating plane velocity and direction?

A vector is a mathematical quantity that has both magnitude (size/length) and direction. In the context of calculating plane velocity and direction, vectors are important because they represent the movement of the plane in a specific direction and at a specific speed.

2. How do you calculate the velocity of a plane using vectors?

The velocity of a plane can be calculated by dividing the displacement vector (change in position) by the time interval. This is known as the average velocity. To calculate the instantaneous velocity, you would take the derivative of the position vector with respect to time.

3. What is the difference between speed and velocity?

Speed is a scalar quantity that refers to the rate of change of distance over time. It does not take into account direction. Velocity, on the other hand, is a vector quantity that refers to the rate of change of displacement over time. It includes both the magnitude and direction of the movement.

4. How can vectors be used to determine the direction of a plane?

Vectors can be used to determine the direction of a plane by representing the plane's position, velocity, and acceleration as vectors. The direction of the plane can then be determined by analyzing the direction of these vectors and how they change over time.

5. How can knowledge of vectors be applied to real-world scenarios involving planes?

Knowledge of vectors can be applied to real-world scenarios involving planes in various ways. For example, it can be used to calculate the optimal flight path for a plane, to determine the impact of wind on a plane's trajectory, or to understand the forces acting on a plane during takeoff and landing. Vectors are also essential in navigation and air traffic control systems.

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