A radar station locates a sinking ship at range 166 km and b

A radar station locates a sinking ship at range 16.6 km and bearing 136° clockwise from north. From the same station, a rescue plane is at horizontal range 19.6 km, 155° clockwise from north, with elevation 1.85 km. Show steps please, it helps me visualize the question.

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

b) How far apart are the plane and ship?

Solution

The coordinates of the ship are 16.6*cos(-46) i + 16.6*sin(-46) j + 0k = 11.53 i - 11.94 j + 0 k

The coordinates of the plane are 19.6*cos(-65) i + 19.6*sin(-65) j + 2.2k = 8.28 i - 17.76 j + 1.85 k

a) Vector from plane to ship is (11.94 - 8.28)i + (-11.94 + 17.75) j + (0 - 1.85) k

so a1 = 3.66

a2 = 5.81

a3 = -1.85

b) distance = sqrt(3.66^2 + 5.81^2 + 1.85^2) = 7.11 km