Solving Plane Displacement Using Radar Data

In summary, the conversation discusses a problem involving a radar station detecting an airplane approaching from the east. The person provides their solution, involving breaking the distance into components and finding the magnitude and direction. However, they are unsure if their calculation is correct and ask for help. Another person suggests using the area of a triangle to solve the problem.
  • #1
Double D Edd
4
0
Okay, this should really be a fairly easy problem and my work is below this question:

"A radar station detects an airplane approaching directly from the east. At first observation, the range to the plane is d1 = 384 m at 40° above the horizon. The airplane is tracked for another 123° in the vertical eastwest plane, the range at final contact being d2 = 770 m. Find the displacement of the airplane during the period of observation."

03_33alt.gif


Heres what I did:

I first figured that the resultant R = d1-d2. So, I decided to break that into components.

Rx = d1x - d2x ; Ry = d1y - d2y. Now, to find the magnitude, I would take the square root of the sum of Rx^2 and Ry^2. And the direction would be the inverse tangent of Ry/Rx.

So, Rx = 384*cos(40) - (-770*Cos(57)). I took the other angle 180-123 = 57. So, Rx = 713.53m

Ry = 384*sin(40) - 770*sin(57). Ry = -398.94 (Which I think is totally wrong).

Now, the rest is pretty simple for me to do provided the above is correct, which I think is not.

I solved this and got the answer for the magnitude as 817.48m. Unfortunately, the answer is wrong.

Know what I am doing wrong here? Thanks :)

Edd.
 
Physics news on Phys.org
  • #2
Take the triangle with sides d1, d2, and let's say d3, which is the displacement of the plane. The area of the triangle equals A = 0.5*d3*h (1), where h = d1*sin40. The area can be expressed as [tex]A=\frac{d_{1}^2 sin(123^{\circ}) sin \gamma}{2sin \alpha}[/tex], where [tex]\gamma[/tex] is the angle between d1 and d3, and [tex]\alpha[/tex] is the angle between d2 and d3. So, calculate the angles, get the area A, and you can get d3 from equation (1). I hope this works.
 
  • #3


I would first like to commend you for your efforts in solving this problem. It is clear that you have a good understanding of the concepts involved and have approached the problem in a logical manner.

However, it seems that there may be some errors in your calculations. For the components, it should be d2x - d1x and d2y - d1y, since the airplane is moving from east to west. Also, the angle for d2x should be 180-123 = 57 degrees, as you mentioned, but for d2y, it should be 90-57 = 33 degrees. This is because the angle between the horizon and the airplane's path is 90 degrees, and the angle of 123 degrees is measured from the east-west plane.

So, the correct calculations would be:

Rx = 770*cos(57) - 384*cos(40) = 104.53 m
Ry = 770*sin(57) - 384*sin(40) = 464.16 m

The magnitude of the displacement would be √(Rx^2 + Ry^2) = √(104.53^2 + 464.16^2) = 477.21 m

And the direction would be the inverse tangent of Ry/Rx = tan^-1(464.16/104.53) = 77.0 degrees.

I believe that your mistake was in the calculation of Ry, and the rest of your steps seem to be correct. I hope this helps and keep up the good work in problem-solving!
 

1. What is radar data and how is it used to solve plane displacement?

Radar data is a type of measurement technology that uses radio waves to detect and track objects in the sky, such as planes. It works by sending out radio waves and then measuring the time it takes for those waves to bounce back to the radar receiver. This information is then used to calculate the position, speed, and direction of the object being tracked.

2. How accurate is radar data in determining the displacement of a plane?

Radar data is highly accurate in determining the displacement of a plane. Modern radar systems have an accuracy of within a few meters, making it a reliable method for tracking and locating planes.

3. What are the potential challenges in using radar data to solve plane displacement?

One challenge in using radar data is the possibility of interference from other objects or weather conditions, which can affect the accuracy of the measurements. Another challenge is the limited coverage of radar systems, as they can only track planes within a certain range.

4. How is radar data used in conjunction with other technologies to solve plane displacement?

Radar data is often used in conjunction with other technologies, such as GPS and satellite imagery, to provide a more comprehensive and accurate picture of plane displacement. These technologies can provide additional information, such as altitude and weather conditions, that can aid in determining the exact location of a plane.

5. How is radar data used in emergency situations involving plane displacement?

In emergency situations, radar data is crucial in quickly locating and tracking planes that may be experiencing difficulties. This information is used by air traffic controllers and other emergency responders to guide pilots and ensure the safety of the plane and its passengers. Radar data can also be used to track debris or other objects that may have fallen from a plane, aiding in search and rescue efforts.

Similar threads

  • Introductory Physics Homework Help
Replies
1
Views
1K
  • Introductory Physics Homework Help
Replies
2
Views
1K
  • Introductory Physics Homework Help
Replies
4
Views
6K
  • Introductory Physics Homework Help
Replies
3
Views
2K
Replies
1
Views
2K
  • Introductory Physics Homework Help
Replies
7
Views
3K
  • Introductory Physics Homework Help
Replies
2
Views
17K
  • Introductory Physics Homework Help
Replies
3
Views
1K
  • Introductory Physics Homework Help
Replies
5
Views
2K
  • Introductory Physics Homework Help
Replies
2
Views
16K
Back
Top