The eye of a hurricane passes over Grand Bahama Island. It is moving in a direction θ = 49° north of west with speed v1 = 41.0 km/h. Exactly three hours later, the course of the hurricane shifts due north, and its speed slows to v2 = 19.5 km/h, as shown below. How far from Grand Bahama is the hurricane 4.0 h after it passes over the island?
I don't think anyone can help here without your map.
It won't let me paste the map :(. I don't even know where to begin.
As it passes over Grand Bahama Island, the
eye of a hurricane is moving in a direction 25
◦
north of west with a speed of 36 km/h. Three
hours later, it shifts due north, and its speed
slows to 30 km/h.
How far from Grand Bahama is the eye 4.50
h after it passes over the island?
Answer in units of km
To find the distance of the hurricane from Grand Bahama Island 4.0 hours after it passes over the island, we can break down the problem into smaller steps.
Step 1: Determine the distance covered by the hurricane in the first 3.0 hours.
Using the formula d1 = v1 * t1, where d1 is the distance, v1 is the velocity (41.0 km/h), and t1 is the time (3.0 hours), we can calculate the distance as:
d1 = 41.0 km/h * 3.0 h = 123.0 km
Step 2: Determine the distance covered by the hurricane in the next 1.0 hour.
Since the hurricane changes its course to due north, the distance covered in the next 1.0 hour is simply given by v2 * t2, where v2 is the new velocity (19.5 km/h) and t2 is the time (1.0 hour). Therefore:
d2 = 19.5 km/h * 1.0 h = 19.5 km
Step 3: Calculate the total distance traveled by the hurricane.
To find the total distance, we need to add the distances covered in step 1 and step 2:
Total distance = d1 + d2 = 123.0 km + 19.5 km = 142.5 km
Therefore, the hurricane is approximately 142.5 km away from Grand Bahama Island 4.0 hours after it passes over the island.