Question

A cruise ship maintains a speed of (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 13 degrees off a direct heading to Barbados. The captain maintains the 23-knot speed for 11 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 23-knot speed is maintained?

          A cruise ship maintains a speed of (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 13 degrees off a direct heading to Barbados. The captain maintains the 23-knot speed for 11 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 23-knot speed is maintained?

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Added by Pilar R.

Precalculus with Limits

Ron Larson 2nd Edition

Instant Answer

Solved by Expert Teresa Fuston

04/22/2022

Step 1

Given that the distance sailed at 23 knots for 11 hours is 253 nautical miles, we can use the Law of Cosines: \[ x^2 = 600^2 + 253^2 - 2(600)(253)\cos(13^\circ) \] \[ x = \sqrt{600^2 + 253^2 - 2(600)(253)\cos(13^\circ)} \] \[ x = \sqrt{360000 + 64009 - 303600 Show more…

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A cruise ship maintains a speed of (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 13 degrees off a direct heading to Barbados. The captain maintains the 23-knot speed for 11 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 23-knot speed is maintained?

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