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?
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Expert's answer
2012-09-13T11:55:02-0400
(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
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