Plane to Ship Displacement (using component method)

[joeseppe]

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

Ship_x=15.4cos123 = -8.39i km
Ship_y=15.4sin123 = 12.92j kmPlane_x=19.4cos150 = -16.8i km
Plane_y=19.4sin150 = 9.7j km
Plane_z=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!

 

[Delphi51]

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.

 

[joeseppe]

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?

 

[Delphi51]

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.

 

[joeseppe]

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:

Ship_x=15.4sin57 = 12.9i
Ship_y=15.4cos57 = -8.39j

Plane_x=19.4sin30 = 9.7i km
Plane_y=19.4cos30 = -16.8j km
Plane_z=2.06k km

Therefore Displacement PtoS = (P-S)
=(-3.20i , -8.41j , 2.06k) km
Right??

 

[Delphi51]

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).

 

[joeseppe]

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! :)

 

[Delphi51]

Most welcome.