The eye of a hurricane passes over Grand Bahama Island. It is moving in a direction θ = 50° north of west with speed v1 = 34.5 km/h. Exactly three hours later, the course of the hurricane shifts due north, and its speed slows to v2 = 16.1 km/h, as shown below. How far from Grand Bahama is the hurricane 3.5 h after it passes over the island?
Given:
v1 = 34.5 [cos(50°) W + sin(50°) N] km/hr
v2 = 16.1 [0 W + 1 N] km/hr
Let: s = 3 v1 + 0.5 v2
Find: |s|
s = (3*34.5*cos(50°)) W + (3*35.6sin(50°)+0.5*16.1) N
|s| = √((3*34.5*cos(50°))^2 + (3*35.6sin(50°)+0.5*16.1)^2)
yes
To answer this question, we need to break it down into two parts - the motion of the hurricane before and after its course shift.
First, let's calculate the distance the hurricane travels before the course shift:
Step 1: Convert the speed from km/h to m/s
v1 = 34.5 km/h = (34.5 * 1000) / 3600 m/s ≈ 9.583 m/s
Step 2: Calculate the distance traveled in three hours
Distance = Speed * Time
d1 = v1 * (3 * 3600) ≈ 9.583 * 10800 m
Next, let's calculate the distance the hurricane travels after the course shift:
Step 1: Convert the speed from km/h to m/s
v2 = 16.1 km/h = (16.1 * 1000) / 3600 m/s ≈ 4.472 m/s
Step 2: Calculate the distance traveled in 3.5 hours
d2 = v2 * (3.5 * 3600) ≈ 4.472 * 12600 m
To find the total distance from Grand Bahama Island, we need to find the sum of the distances traveled before and after the course shift:
Total Distance = d1 + d2
Now, substitute the calculated values and solve:
Total Distance ≈ (9.583 * 10800) + (4.472 * 12600) meters
Evaluating this expression will give you the distance from Grand Bahama Island to the hurricane 3.5 hours after it passes over the island.