A cruise ship maintains a speed of 19 knots19 knots nautical

A cruise ship maintains a speed of 19 knots19 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 18 degrees18° off a direct heading to Barbados. The captain maintains the 19 dash knot19-knot speed for 1515 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 19 dash knot19-knot speed is maintained?

Solution

By using law of cosines to find length across from 18 degree

Then speed=19×10=190

C^2=a^2+b^2-2abcosc

C^2 =190^2+600^2-2×190×600cos18

C^2=179259.11

C=423.3nautical miles

Use law of some to find the angle of head to Barbados

SinA/a=sinB/b

Sin18degree/423.39=sinB/600

SinB=0.4391

B=26.04degree

The degree of barbadose is 26.04 degree.

b) Now we have to convert into time at 19knots/hour

423.39/19=22.28 hr