Question

A radar station locates a sinking ship at range 17.3 km
and bearing 136° clockwise from north. From the same
station a rescue plane is at horizontal range 19.6 km,
153° clockwise from north, with elevation 2.20 km.
(a) Write the vector displacement from plane to ship,
letting i represent east, j north, and k up. (b) How far
apart are the plane and ship?

Answer 1

@mikaela19900630

Answer 2

for a)
Converting to CCW from + x axis
360-(136-90) = 314
360-(153-90) = 297

Position vector of ship relative to origin:
17.3* Cos( 314) i+ 17.3* Sin( 314) j
or
Rs = <12.02 i , -12.44 j , 0k>

Position vector of plane relative to origin "below" :
19.6* Cos( 297) i+ 19.6* Sin( 297) j
or
Rp = <8.90 i , -17.46 j , 2.2 k>


Rsp = Rso - Rpo
=
12.02 - 8.90 = 3.12i km "east"
-12.44 - (-17.46) = 5.02j km "north"
0 - 2.2 = -2.2k km "below"

The plane sees the ship at:
Rsp =<3.12i , 5.02j , -2.2k> km

Answer 3

For b) |R| = sqr(3.12^2+(5.02)^2 + (-2.2)^2) = 6.307 km