A cruise ship maintains a speed of 12 knots12 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 26 degrees26° off a direct heading to Barbados. The captain maintains the 12 dash knot12-knot speed for 88 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 12 dash knot12-knot speed is maintained?

a) The angle through which the captain has to turn = 27°

b) It will take the ship 48.3 hours to reach Barbados from what the turn is made

Explanation:

The image of the situation is attached to the question.

The distance travelled by the captain moving at 12 knots for 88 hours = 12 × 88 = 1056 nautical miles.

Let θ represent the angle through which the captain has to turn.

And let the distance between when the captain turns and Barbados be d.

Using cosine rule,

d² = 1056² + 600² - 2(1056)(600) cos 26°

d² = 336,184.185

d = 579.8 nautical miles.

a) To obtain the angle through which the captain has to turn, θ, we use the sine rule

[(Sin θ)/600] = [(sin 26°)/579.8]

Sin θ = (600 × sin 26°)/579.8

sin θ = 0.4536

θ = 27°

b) Barbados is now 579.8 nautical miles away, travelling at 12 knots,

Speed = (Distance/time)

Time = (distance/speed) = (579.8/12)

Time = 48.3 hours

Hope this Helps!!!

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