Thread: Graphing

The weather service is tracking Hurricane Jeffery on a grid map with coordinate units representing 10 miles. At 10:00 a.m., the center of the hurricane is located at (3, -4). Hurricane-force winds extend 70 miles out from the center. It is predicted that the eye of Jeffrey will be located at (-1, -2) in two hours. Your cabin by Lake Helen is located on the grid map at (-7, -5). Will you feel the force of the hurricane winds at noon? What is the predicted rate (in miles per hour) of the movement of the eye of Jeffrey?

To find if I would feel the hurricane winds at noon, do I find the square root of,
[-10-(-70)]^2 + [(-20-(-50)]^2 ?

How would I find the "predicted rate (in miles per hour) of the movement of the eye of Jeffrey?"

Originally Posted by Ash

The weather service is tracking Hurricane Jeffery on a grid map with coordinate units representing 10 miles. At 10:00 a.m., the center of the hurricane is located at (3, -4). Hurricane-force winds extend 70 miles out from the center. It is predicted that the eye of Jeffrey will be located at (-1, -2) in two hours. Your cabin by Lake Helen is located on the grid map at (-7, -5). Will you feel the force of the hurricane winds at noon? What is the predicted rate (in miles per hour) of the movement of the eye of Jeffrey?

To find if I would feel the hurricane winds at noon, do I find the square root of,
[-10-(-70)]^2 + [(-20-(-50)]^2 ?

How would I find the "predicted rate (in miles per hour) of the movement of the eye of Jeffrey?"

Hello,

the hurricane "travels" in 2 hours from (3, -4) to (-1, -2). the distance is:

d = √((-1-3)² + (-2 - (-4))²) = √(16 + 4) = √(20) ≈ 4.472

according to the scale of the map 44.72 mi. That means the "rate of the movement" (normally you call it speed) is 22.36 mi/h.

At noon the hurricane is at (-1, -2) and your cabin is at (-7, -5). You only have to check if the cabin is within the 70-miles-range of the hurricane:

s = √((-7-(-1))² + (-5 - (-2))²) = √(36 + 9) = √(45) ≈ 6.708
according to the scale of the map 67.08 mi. So you'll feel the force of the hurricane.

If the hurricane has some mathematical properties you can describe the way of the hurricane as a straight line: y = -1/2*x - 5/2.
The the shortest distance between your cabin and the eye of the hurricane will be reached a few minutes before 2:00pm and the eye is only 53.67 mi away.

I've attached a diagram to show you the situation. The circles are the boundaries of the 70-miles-range of the wind field.

EB