The eye of a hurricane passes over Grand Bahama Island in a direction 60.0° north of west with a speed of 36.1 km/h. Three hours later, the course of the hurricane suddenly shifts due north, and its speed slows to 26.9 km/h. How far (in km) from Grand Bahama is the hurricane 4.6 h after it passes over the island?
To find the distance of the hurricane from Grand Bahama 4.6 hours after passing over the island, we can break the problem into two parts:
Part 1: The Distance Covered during the first 3 hours
During the first three hours, the hurricane is moving in a direction 60.0° north of west with a speed of 36.1 km/h. To find the distance covered during this time, we use the formula:
Distance = Speed × Time
Distance_1 = 36.1 km/h × 3 h
Part 2: The Distance Covered during the next 1.6 hours
After the course of the hurricane suddenly shifts due north, it continues for 1.6 additional hours at a speed of 26.9 km/h. To find the distance covered during this time, we again use the formula:
Distance = Speed × Time
Distance_2 = 26.9 km/h × 1.6 h
Total Distance = Distance_1 + Distance_2
Total Distance = (36.1 km/h × 3 h) + (26.9 km/h × 1.6 h)
Finally, we can calculate the Total Distance covered by the hurricane 4.6 hours after passing over the island.