Distance of Hurricane from Grand Bahama Island: 104 km

[mortho]

Homework Statement

The eye of a hurricane passes over Grand Bahama Island. It is moving in a direction 60.0° north of west with a speed of v1 = 37.0 km/h. Exactly three hours later, the course of the hurricane shifts due north, and its speed slows to v2 = 27.0 km/h, as shown in Figure 3-30. How far from Grand Bahama, in kilometers, is the hurricane 4.50 h after it passes over the island?

Homework Equations

sine, cosine

The Attempt at a Solution

i ended up getting 104 km using tangent to find the angle then using the angle and opposite to find adgacent which i got 104. the sides were 111km and 40.5 km after multiplying with the velocity conversion.

 

[Anadyne]

I don't think you need to find the angle of anything. I agree that the total distances traveled are 111 and 40.5. Keep in mind that these have a certain direction. The real problem is the first one because it has north and west components. If you can figure out what those are, then you can add the second displacement to the north component. With the total north and west displacements, you can use the pythagorean theorem to find the total distance away.

 

[ogb p]

Your solution using trigonometry to find the distance of the hurricane from Grand Bahama Island is correct. However, it would be beneficial to also consider the direction and speed of the hurricane in your solution. The direction of the hurricane shifted from 60.0° north of west to due north, which means the angle of movement also changed. This could affect the final distance calculation. Additionally, you could also consider using the Pythagorean theorem to find the total distance traveled by the hurricane in the given time frame. Overall, your approach is valid and the resulting distance of 104 km is accurate.