A cruise ship maintains a speed of 12 knots nautical miles p

A cruise ship maintains a speed of 12 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 32 degree off a direct heading to Barbados The captain maintains the 12-knot speed for 7 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-knot speed is maintained? (a) Through what angle should the captain turn to head directly to Barbados? The captain should head through an angle of degree (b) Once the turn is made how long will it be before the ship reaches Barbados if the same 12-knot speed is maintained? The time it will take for the ship to reach Barbados is hours.

Solution

Find the distance traveled. 12(7) = 84 nautical miles

Find the distance remaining. d² = 600² + 84² - ­ 2(600)(84)cos32 ==========> d = 530.6 nautical miles

Find the angle towards Barbados.

sinS/600 = sin32/530.6

S = 36.8 degree =  the angle the captain should turn

b) .we already found the distance to be 530.6 nautical miles. Now we haveto convert that into time at 15 knot/hour.

530.6/12 = 44.22 hours