A Coast Guard cutter detects an unidentified ship at a distance of 18.0 km in the direction 15.0°

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 56.0 km/h, in what direction should it head? Express the direction as a compass bearing with respect to due north.

 

Your response differs from the correct answer by more than 10%. Double check your calculations.° east of north

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

Answer 1

Hi Ashlynn W.,

You know from general experience that there must be a unique solution, therefore the problem should be solvable algebraically. Let's assume that your problem is in setting up the problem for math treatment, and see how you would go about setting up the equations to solve. Call the present position of the cutter (0,0) in a Cartesian (x,y) map representation.

then the present position of the IDK ship is (18cos75°, 18sin75°). The IDK ship's position will be (x,y)_t = (x,y)₀ + t*(23cos50°,23sin50°). This must intercept the speedboat, which is travelling at (x,y)_t = 56t(cosθ,sinθ) .

That's 2 equations (one for x coordinates, one for y coordinates) to satisfy 2 unknowns.

If you need that broken out more explicitly:

18cos75°+23t*cos50° = 56t*cosθ (for the x = east displacement) and

18sin75° + 23t*sin50° = 56t*sinθ (for the y = north displacement).

You should be able to substitute in the known values, separate variables, and solve for t and then θ .? (You are, of course, given the latitude to solve the problem in any other way you see fit!)

-- Cheers, -- Mr. d.