# Solve Dynamics Problem: Calculate x- and y-components of Position & Velocity

• hkapoor
In summary, the conversation discusses tracking an airplane using two radar stations located a distance of 1600 m apart. The stations can measure the angle of the airplane and its rate of change. The data provided includes the distance and angles of the airplane, as well as its angular velocities. The conversation also suggests using trigonometry to determine the x and y coordinates of the airplane's position.
hkapoor
Any help would be appreciated. Thanks.

An airplane is being tracked by two radar station which are a distance "s" apart from each other. Each radar station can measure the angle between the horizontal and the line from the station to the airplane and can measure the rate of change of the angle.

Distance s = 1600 m

Angles :
α = 40 o
β = 60 o

Angular velocities :
alpha= 1.7 o/sec
beta= 2.7 o/sec

Enter the x- and y-component of the position :

Enter the x- and y-component of the velocity :

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Welcome to PF

For starters, try drawing a right triangle using the angle α and the point M. Then use what you know about trig to relate α and the x,y coordinates of M.

I don't have the x,y coordinates of M. just the distance from point 1 to 2.

For now, the x,y coordinates of M are just "x" and "y". The idea is to set up some equations from which you can figure out their values.

## 1. How do you calculate the x- and y-components of position?

To calculate the x- and y-components of position, you will need to use the Pythagorean theorem. First, you will calculate the hypotenuse of the triangle formed by the x- and y-components, which represents the total displacement. Then, you can use trigonometric functions to find the x- and y-components.

## 2. What are the units for the x- and y-components of position?

The units for the x- and y-components of position will depend on the units used for the total displacement. If the total displacement is given in meters, then the x- and y-components will also be in meters.

## 3. How can you determine the velocity from the x- and y-components?

To determine the velocity from the x- and y-components, you will need to use the Pythagorean theorem again. The total velocity will be the hypotenuse of the triangle formed by the x- and y-components. You can then use trigonometric functions to find the direction of the velocity.

## 4. Can you solve for the x- and y-components of velocity without knowing the position?

Yes, you can solve for the x- and y-components of velocity without knowing the position. Velocity is defined as the rate of change of position, so you can use the formula for average velocity to calculate its components. This only requires knowing the initial and final positions.

## 5. How do you handle negative values in the x- and y-components of position and velocity?

Negative values in the x- and y-components of position and velocity indicate direction. A negative x-component means the object is moving to the left, while a negative y-component means the object is moving downwards. It is important to include the negative sign in the calculation and interpretation of these values.

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