Physics please help

[Crank]

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Hey, can you guys help me on this physics problem from my test prep book? It seems pretty basic but I'm just not getting the right answer.

Here it is:

A Coast Guard cutter detects an unidentified ship at a distance of 16.0 km in the direction 15.0° east of north. The ship is traveling at 22.0 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 44.0 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.

Any help would be greatly appreciated.

 

[h9i9j9]

I used sine law on the triangle.

First I let t be the amount of time in hours it would take to intercept the boat. This give you a triangle with one defined length and 2 variable length (well, length that have t in them, they're not exactly variable...see part b).
Using sine law, the two t's will cancel and then we get the angle to be sent out to be 31.7 degrees E of N. Another sine law will help you solve the amount of time taken. I got 0.663 hours.

Is this the answer in your book?
Hope that help!🙂

 

[Crank]

Answers are (a) 27.2 degrees and (b) 41.6 mins

 

[h9i9j9]

hmm, interesting.... did you get what I got?