Assume that the Grand Bahama Island lies at the origin of the coordinate system shown in the diagram at below. Vector represents the hurricane's displacement at 44.5 km/h and vector represents its displacement after it shifts course three hours later and proceeds at a speed of 23.5 km/h. Vector represents the hurricane's displacement after a total time of 4.95h.
To solve this problem, we can use vector addition and subtraction to find the net displacement of the hurricane.
First, let's break down the given information into individual vectors:
1. Vector A represents the initial displacement of the hurricane at a speed of 44.5 km/h.
2. Vector B represents the displacement of the hurricane after it shifts course, at a speed of 23.5 km/h.
3. Vector C represents the total displacement of the hurricane after 4.95 hours.
Now, we need to find the net displacement of the hurricane by adding or subtracting the vectors.
Since the Grand Bahama Island is at the origin, vector A starts at (0, 0).
Vector B represents the displacement after the hurricane shifts course three hours later. To find the coordinates for vector B, we need to calculate the distance traveled during those three hours. As the hurricane is moving at a constant speed of 44.5 km/h, we can calculate the distance using the formula:
Distance = Speed × Time
Distance = 44.5 km/h × 3 hours
Distance = 133.5 km
Therefore, vector B starts at (133.5, 0) on the coordinate system.
Vector C represents the total displacement after 4.95 hours. To find the coordinates for vector C, we need to calculate the distance traveled during the remaining 4.95 - 3 = 1.95 hours. As the hurricane is now moving at a constant speed of 23.5 km/h, we can calculate the distance using the same formula:
Distance = Speed × Time
Distance = 23.5 km/h × 1.95 hours
Distance = 45.825 km
To find the final position of vector C, we add the distance traveled during the first three hours (133.5 km) to the distance traveled during the remaining 1.95 hours (45.825 km).
Therefore, vector C starts at (133.5 + 45.825, 0) on the coordinate system.
By adding vectors A, B, and C, we can find the net displacement of the hurricane. However, we need to consider the directions as well. Since all vectors start from the origin, their x-components will be positive, and their y-components will be zero.
The x-component of vector A is 44.5 km/h * 4.95 hours = 220.275 km.
The y-component of vector A is 0 km.
The x-component of vector B is 23.5 km/h * 1.95 hours = 45.825 km.
The y-component of vector B is 0 km.
The x-component of vector C is 0 km.
The y-component of vector C is 0 km.
Now, let's add the x-components and y-components separately to find the net displacement:
x-component = 220.275 km + 45.825 km + 0 km = 266.1 km
y-component = 0 km + 0 km + 0 km = 0 km
Therefore, the net displacement of the hurricane after a total time of 4.95 hours is (266.1, 0) on the coordinate system.