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 23.0 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 58.0 km/h, in what direction should it head? Express the direction as a compass bearing with respect to due north.
_________ ° east of north

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

Explanation / Answer

(a) SOLUTION: Location of the ship, r= 18 km cos15o                                     =17.83 km speed of the ship,    v= (23 km/h) cos40o                                     =17.61 km/h required time , t = r/v                            = 1.01 h t = 1.01 hr, at point of interception,
distance traveled by ship ,                                          = (17.61 km/h)(1.01 h)                                          = 17.78 km
distance traveled by speedboat,                                         = (58 km/h)(1.01 h)                                          = 57.42 km thus, from free- body diagram, we have    sin()/ 17.78 km = sin(40 )/57.42 km                              = 11.48o east of north.

                                    =17.83 km speed of the ship,    v= (23 km/h) cos40o                                     =17.61 km/h required time , t = r/v                            = 1.01 h                                     =17.61 km/h required time , t = r/v                            = 1.01 h t = 1.01 hr, at point of interception,
distance traveled by ship ,                                          = (17.61 km/h)(1.01 h)                                          = 17.78 km
distance traveled by speedboat,                                         = (58 km/h)(1.01 h)                                          = 57.42 km thus, from free- body diagram, we have    sin()/ 17.78 km = sin(40 )/57.42 km                              = 11.48o east of north.

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