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College Physics

11th Edition
Raymond A. Serway + 1 other
ISBN: 9781305952300

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College Physics

11th Edition
Raymond A. Serway + 1 other
ISBN: 9781305952300
Textbook Problem

A Coast Guard cutter detects an unidentified ship at a distance of 20.0 km in the direction 15.0° cast of north. The ship is traveling at 26.0 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 50.0 km/h, in what direction should it head? Express the direction as a compass bearing with respect to due north, (b) Find the time required for the cutter to intercept the ship.

(a)

To determine
The direction of the speed boat.

Explanation

As shown in the figure, the y axis is lying at 15.0° east of north.

Let the original displacement be d0 . During the time t required for the cutter to intercept the ship, the ship undergoes displacement ds and the cutter undergoes displacement dc .

The magnitude of d0 is 20.0km , ds is (26.0km/h)t and dc is (50.0km/h)t .

Equating the x components of the vectors,

dcsinα=dssin25.0°

Substitute ds for (26.0km/h)t and dc for (50

(b)

To determine
The time required for the cutter to intercept the ship.

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