A cruise ship maintains a speed of 17 knots ?(nautical miles per? hour) sailing

Question

A cruise ship maintains a speed of 17 knots ?(nautical miles per? hour) sailing from San Juan to? Barbados, a distance of 600 nautical miles. To avoid a tropical? storm, the captain heads out of San Juan at a direction of 19 degrees off a direct heading to Barbados. The captain maintains the 17 dash knot speed for 14 ?hours, after which time the path to Barbados becomes clear of storms. ?

(a) Through what angle should the captain turn to head directly to? Barbados? ?

(b) Once the turn is? made, how long will it be before the ship reaches Barbados if the same 17 dash knot speed is? maintained?

Explanation / Answer

Solution :-first We will use the law of cosines to find length across from 19 deg.
c^2 = a^2+b^2-2ab COS(C) { here a =14 *17 =238 }
c^2= 238^2 + 600^2 - (2)(238)(600) cos(19)
c= 382.8888

, 'c' is the side 382.88 = 383 nautical miles.

Now,we use the law of sines to find the angle to head to barbados .
SinA/a = SinB/b
Sin(19 deg)/383= SinB/600 solve for SinB
B = 30.6657 deg. = 30.7 degree

b) time = Time=Distance/Speed. 383 nautical miles / 17knots = 22.5

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