How Far Is the Hurricane From Grand Bahama After 4.5 Hours?

[CelebrityRose000]

I just don't get this problem one bit...i've tried drawing a picture too and it doesn't help ...here it is if someone can help!

The eye of a hurricane passes over Grand Bahama Island. It is moving in a direction 60 degrees north of west with a speed of 41 km/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 4.50 h after it passes over the island?

help please! and fast!

 

[Astronuc]

You have time, velocity and direction, so you need to determine the two vectors, which added together will identify the location.

The Grand Bahama is the origin. You are given that in three hours, during which the eye moves at 45 km/h in the direction 60° from due west (-x). So determine that vector.

Between 3 hrs and 4.5 hrs (or 1.5 hrs) the eye moves north at 25 km/h. The tail of that vector starts head of the first vector. Due north is +y direction.

Add the two vectors to find the location. The magnitude of the resulting vector is the distance.

 

[wais]

The components of a vector refer to its magnitude and direction. In this problem, the magnitude of the vector is the speed of the hurricane, which is given as 41 km/h when it is moving in a direction 60 degrees north of west. This means that the hurricane is moving at a speed of 41 km/h in a direction that is 60 degrees counterclockwise from the west direction.

After three hours, the course of the hurricane shifts due north, which means it is now moving directly north. The speed also changes to 25.0 km/h. This means that the magnitude of the vector is now 25.0 km/h, and its direction is north.

To find the distance the hurricane has traveled after 4.50 hours, we need to use the formula: distance = speed x time. In this case, the speed is the magnitude of the vector, which is 25.0 km/h, and the time is 4.50 hours. This gives us a distance of 112.5 km.

To visualize this, you can draw a diagram with the initial vector (41 km/h at 60 degrees north of west) and the final vector (25.0 km/h due north). The distance between the initial and final points will give you the distance the hurricane has traveled, which is 112.5 km.

I hope this helps you understand the problem better. It's important to understand the components of a vector in order to solve problems like this. Don't get discouraged, keep practicing and you'll get the hang of it!