Question

A radar station locates a sinking ship at range 17.5 km and bearing 136° clockwise from north. From the same station, a rescue plane is at horizontal range 19.6 km, 169° clockwise from north, with elevation 2.40 km.
(a) Write the displacement vector from plane to ship, letting represent east, north, and up.
(b) How far apart are the plane and ship?

Answer 1

(a) Write the displacement vector from plane to ship, letting
represent
east, north, and up.
From station to ship:
East: 17.5 * sin(136°) =
12.156 km
North: 17.5 * cos(136°) = -12.588 km
Up: 0 km
From station to
plane:
East: 19.6 * sin(169°) = 3.740 km
North: 19.6 * cos(169°) = -19.240
km
Up: 2.4 km
From plane to ship:
East: 17.5 * sin(136°) = 12.156
km
North: 17.5 * cos(136°) = -12.588 km
Up: 0 km
From station to
plane:
East: 19.6 * sin(169°) = - 8.416 km
North: 19.6 * cos(169°) = -
6.652 km
Up: 2.4 km
(b) How far apart are the plane and ship?
At
horizontal range: Lh = sqrt( (- 8.416)^2 + (-6.652)^2 ) = 10.727 km
At all L=
sqrt( Lh^2 + 2.4^2 ) = 10.993 km