Plane to Ship Displacement (using component method)

In summary, the problem involves finding the vector displacement from a plane to a ship located at a certain range and bearing from a coastguard station. Using the given equations and information, the displacement is calculated to be (3.2i, 8.41j, -2.06k) km, where i represents east, j represents north, and k represents up.
  • #1
joeseppe
28
0

Homework Statement


A coastguard station locates a ship at range 15.4 km and bearing 123° clockwise from north.

From the same station a plane is at horizontal range 19.4 km, 150° clockwise from north, with elevation 2.06 km.

What is the vector displacement from plane to ship, let i represent east, j north, and k up.

Homework Equations


The Attempt at a Solution


Shipx=15.4cos123 = -8.39i km
Shipy=15.4sin123 = 12.92j kmPlanex=19.4cos150 = -16.8i km
Planey=19.4sin150 = 9.7j km
Planez=2.06 k km

Therefore Displacement PtoS = (P-S)
=(-8.41i , -3.22j , 2.06k) km

Any help you could give me would be greatly appreciated!
 
Last edited:
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  • #2
Shipx=15.4cos123 = -8.39i km
Shipy=15.4sin123 = 12.92j km
You seem to have these reversed; the sine gives the i (east) value.
 
  • #3
Delphi51 said:
You seem to have these reversed; the sine gives the i (east) value.

Really? So Sin is for the X direction, and cos is for the Y? That's not what my textbook says?
 
Last edited:
  • #4
I hate to make a general statement about this with angles greater than 90 degrees.
But if you draw the diagram and note that the ship is 57 degrees away from the south line, then you would naturally say that sin(57) = x/15.4 so x = 15.4*sin(57) = 12.9 to the east.
 
  • #5
Delphi51 said:
I hate to make a general statement about this with angles greater than 90 degrees.
But if you draw the diagram and note that the ship is 57 degrees away from the south line, then you would naturally say that sin(57) = x/15.4 so x = 15.4*sin(57) = 12.9 to the east.
Yeah I did draw a diagram, I just don't have a scanner to upload it.
I never thought to look at it as two triangles though.

So what I actually should have is:

Shipx=15.4sin57 = 12.9i
Shipy=15.4cos57 = -8.39j

Planex=19.4sin30 = 9.7i km
Planey=19.4cos30 = -16.8j km
Planez=2.06k km

Therefore Displacement PtoS = (P-S)
=(-3.20i , -8.41j , 2.06k) km
Right??
 
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  • #6
Therefore Displacement PtoS = (P-S)
=(-3.20i , -8.41j , 2.06k) km
Hmm, from the plane you would have to go east, north and down to get to the ship.
Therefore I think it should be (3.2i, 8.41j, -2.06k).
 
  • #7
Delphi51 said:
Hmm, from the plane you would have to go east, north and down to get to the ship.
Therefore I think it should be (3.2i, 8.41j, -2.06k).

Makes sense. Thanks again for the help! :)
 
  • #8
Most welcome.
 

1. What is the component method for calculating plane to ship displacement?

The component method is a mathematical approach used to determine the displacement of a plane to a ship. It involves breaking down the velocity vector of the plane into its horizontal and vertical components, and then using these components to calculate the displacement of the plane relative to the ship.

2. How is the component method different from other methods of calculating displacement?

The component method differs from other methods because it takes into account the specific direction of the plane's velocity in relation to the ship. It provides a more accurate measurement of the displacement, as it considers both the horizontal and vertical movement of the plane.

3. What factors affect the accuracy of the component method for plane to ship displacement?

The accuracy of the component method is affected by several factors, including the precision of the measurements of the plane's velocity, the distance between the plane and the ship, and any external forces acting on the plane or ship that could alter their movement.

4. Can the component method be used to calculate displacement for any type of plane and ship?

Yes, the component method can be applied to any type of plane and ship, as long as the necessary measurements and calculations are available. However, some adjustments may need to be made for unique situations, such as extreme weather conditions or unusual flight paths.

5. Are there any limitations to using the component method for plane to ship displacement?

While the component method is generally a reliable approach for calculating displacement, it does have some limitations. It assumes that the plane and ship are moving in a straight line and at a constant speed, which may not always be the case. Additionally, it does not take into account any external factors that could affect the movement of the plane or ship.

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