Calculating Hurricane Distance with Vectors

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In summary, a hurricane passing over Grand Bahama Island at a speed of 41.0km/h in a direction 60.0 degrees north of west suddenly shifts its course to due north with a speed of 25.0 km/h. After 4.5 hours, the hurricane will be located a distance away from Grand Bahama Island, which can be determined through vector calculations and graphically by drawing a line in the direction of the hurricane's path.
  • #1
Maddy315
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The eye of a hurricane passes over Grand Bahama Island in a direction 60.0 degrees north of west with a speed of 41.0km/h. Three 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 4.5 h after it passes over the island?

I know we're going over v=d/t but my teacher didn't have time to fully explain.
I'm completely confused and I'm not so sure that my picture came out right either. Help?

b]
 
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  • #2
Maddy315 said:
The eye of a hurricane passes over Grand Bahama Island in a direction 60.0 degrees north of west with a speed of 41.0km/h. Three 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 4.5 h after it passes over the island?

I know we're going over v=d/t but my teacher didn't have time to fully explain.
I'm completely confused and I'm not so sure that my picture came out right either. Help?

b]

SO what did you calculate, and at least describe your picture - [like the first arrow is like a clock hand pointing to 9:00, then one from there pointing at 6:00 but hopefully not either of those directions]
 
  • #3
Like everything else in life, the best way to do it is through vectors.

And graphicall would be the best way to see it, so start by drawing a line going in the first direction, and then a line going in the second starting from the tip of the first.

The line between the tip of the second and the start will be your answer, graphically.
 

FAQ: Calculating Hurricane Distance with Vectors

What is a vector?

A vector is a mathematical object that has both magnitude (size) and direction. It is represented by an arrow in a coordinate system, with the length of the arrow representing the magnitude and the direction of the arrow representing the direction.

How do you find the length of a vector?

To find the length of a vector, you can use the Pythagorean theorem. This involves finding the square root of the sum of the squares of the individual components of the vector. Alternatively, you can use the magnitude formula, which involves finding the square root of the dot product of the vector with itself.

What is a unit vector?

A unit vector is a vector that has a length of 1. It is often used to represent a direction or a basis vector in a particular coordinate system.

How do you find the direction of a vector?

The direction of a vector can be found by taking the inverse tangent of the vertical component over the horizontal component. This will give you the angle of the vector in reference to the positive x-axis.

Can vectors be added or subtracted?

Yes, vectors can be added or subtracted by adding or subtracting their individual components. This is known as vector addition or vector subtraction, and the resulting vector is called the resultant vector.

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