A Coast Guard cutter detects an unidentified ship at a distance of 18.0 km in th

Question

A Coast Guard cutter detects an unidentified ship at a distance of 18.0 km in the direction 15.0° east of north. The ship is traveling at 21.0 km/h on a course at 40.0° east of north. The Coast Guard wishes to send a speedboat to intercept and investigate the vessel.
(a) If the speedboat travels at 60.0 km/h, in what direction should it head? Express the direction as a compass bearing with respect to due north.
1 ° east of north

(b) Find the time required for the cutter to intercept the ship.
2 min

Explanation / Answer

choose the x axis along the 18 km distance the y- componnet of the displacement of the ship agree    (20 km/h) t sin(40.00 - 15.00) = (40 km/h) t sin             8.45km/h = 40 km/h sin                       = sin-1(8.45 km/h/ 40 km/h)                           =12.190
the speeed of the boat shoul head            15.00 + 12.190 = 27.190 the direction is east of north. the direction is east of north.

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