Displacement Vector Question?

Question

Need help solving this problem!

A radar station locates a sinking ship at range 18.3 km and bearing 136° clockwise from north. From the same station, a rescue plane is at horizontal range 19.6 km, 167° clockwise from north, with elevation 2.55 km.

(a) Write the displacement vector from plane to ship, letting i hat represent east, j hat north, and k hat up.

(i hat + j hat + k hat) km

(b) How far apart are the plane and ship?

Answer in km

Answer 1

set radar station to origin of coordinates

position of ship = -18.3cos 46 i -18.3sin46 j +0k

position of plane = -19.6cos77 i -19.6 sin 77 j + 2.55 k

displacement vector between plane and ship =

position of plane - position of ship =

(18.3cos46-19.6cos77)i+(18.3sin46-19.6 sinyy)j +2.55k

evaluate the i, j and k components

the total distance = sqrt[i component^2+j component^2+ k component^2]