Solve Vector Problem: Hurricane Path & Distance from Grand Bahama

In summary, the eye of a hurricane passed over Grand Bahama Island and then shifted direction and slowed down after 3 hours. To calculate its distance from the island after 4.50 hours, you can use trigonometry to determine the horizontal and vertical components of its movement.
  • #1
Malicious
16
0
The eye of a hurricane passes over Grand Bahama Island. It is moving in a direction of 60.0 (degrees) north of west with a speed of 41.0 km/h. 3 hours later, the course of the hurricane suddenly shifts due north, and its speed slows to 25.0 km/h. How far from Grand Bahama is the hurricane 4.50 h after it passses over the island?

How do I begin to solve this problem? I can't seem to find examples in the book that show how to solve this problem.
 
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  • #2
Initially, you have a direction, a velocity and a time. How far has been moved horizontally and vertically ?
Ditto after the hurricane shifts.
Add the x- and y-values together.
 
  • #3
Trig

Break it into the x and y conponents using trig. For instance, If the storm moved up at a NNW direction for one hour at a speed of 5 miles an hour then you know that the angle is 45 degrees and the length of the hypotenuse is five miles. Elementry trig will give you the x and y.
 

FAQ: Solve Vector Problem: Hurricane Path & Distance from Grand Bahama

What is a vector problem?

A vector problem is a mathematical problem that involves the use of vectors, which are quantities that have both magnitude and direction. In the context of a hurricane path and distance from Grand Bahama, vectors can be used to represent the direction and speed of the hurricane's movement.

How can vectors be used to solve a hurricane path problem?

Vectors can be used to represent the direction and speed of the hurricane's movement. By breaking down the hurricane's movement into smaller vectors, such as its velocity and acceleration, we can calculate the overall path of the hurricane and determine its distance from Grand Bahama.

What information is needed to solve a vector problem involving a hurricane path?

To solve a hurricane path problem using vectors, we need to know the initial position of the hurricane, its velocity, and any external factors that may affect its movement (such as wind patterns or land masses).

What is the importance of solving a vector problem for predicting a hurricane's path?

Solving a vector problem for a hurricane's path is important because it allows us to accurately predict the trajectory and potential impact of the hurricane. This information can be crucial for disaster preparedness and planning evacuation routes.

Can vectors be used to solve other types of natural disaster problems?

Yes, vectors can be used to solve a variety of natural disaster problems. For example, they can be used to predict the path of a tornado or the direction and speed of a river's current during a flood. Vectors are a useful tool for understanding and predicting the movements of many natural phenomena.

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