A Coast Guard cutter detects an unidentified ship at a distance of 22.0km in the

Question

A Coast Guard cutter detects an unidentified ship at a distance of 22.0km in the direction 15.0° east of north. The ship is traveling at 25.0km/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 54.0 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

I believe you need the velocity of the speedboad in order to solve this. (The timeframe to interception would be satisfactory.) The approach will be to get the ship's location as a function of time. Initially, y = 21km * cos15º = 20.3 km x = 21km * sin15º = 5.44 km y(t) = 20.3km + 22km/h * cos40º * t x(t) = 5.44km + 22km/h * sin40º * t assuming you had the speedboat's speed, you could create similar eqn's of motion: Y(t) = .... X(t) = .... both also functions of some unknown angle T You need to have a time t such that y(t) = Y(t) and x(t) = X(t) You'll have 2 eqns and 2 unknowns (t and T) and can solve. May require some trig substitution.

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