3.8. A radar station locates a sinking ship at range 17.3 km and bearing 136 deg

Question

3.8. A radar station locates a sinking ship at range 17.3 km and bearing 136 degrees
clockwise from north. From the same station a rescue plane is at horizontal range
20.7 km, 153 degrees clockwise from north, with elevation 2.20 km.
(a) The vector displacement from plane to ship can be written in the form,
a1i+a2j+a3k, where i represents east, j represents north, and k represents up. Find the
values of
(a) a1, (km)
(b) a2, (km)
(c) a3. (km)
(d) Also, nd the distance between the plane and the ship (km).

Explanation / Answer

x1 = 17.3 cos 136 = -12.4 km x-component of ship y1 = 17.3 sin 136 = 12.0 km y-component of ship x2 = 20.7 cos 153 = -18.4 km x-component of plane y2 = 20.7 sin 153 = 9.40 km y-component of plane z2 = 2.2 km (x1 - x2) i + (y1 - y2) j + (z1 - z2) k vector displacement of plane to ship (-12.4 + 18.4) i + (12 - 9.4) j + (0 - 2.2) = a1 i + a2 j + a3 k 6 i + 2.6 j -2.2 k = vector displacement from plane to ship D = (6^2 + 2.6^2 + 2.2^2)^1/2 = 6.90 km from plane to ship

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