We appreciate your visit to A ship leaves a port on a bearing of 28º and travels 8 2 miles The ship then turns due east and travels another 4. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!
Answer :
Final answer:
To find the distance from the ship to the port, we can use trigonometry and vector addition. The ship is approximately 8.32 miles from the port.
Explanation:
To solve this problem, we can use trigonometry and vector addition. Let's start by finding the component vectors for each leg of the ship's journey. The ship travels 8.2 miles on a bearing of 28º, so the horizontal component is 8.2*cos(28º) = 7.34 miles and the vertical component is 8.2*sin(28º) = 3.84 miles. After the ship turns due east and travels 4.3 miles, the horizontal component remains the same, but the vertical component becomes 0 since the ship is now traveling east. To find the distance from the ship to the port, we can use the Pythagorean theorem: distance = [tex]sqrt((7.34)^2 + (3.84)^2)[/tex] = 8.32 miles. Therefore, the ship is approximately 8.32 miles from the port.
Thanks for taking the time to read A ship leaves a port on a bearing of 28º and travels 8 2 miles The ship then turns due east and travels another 4. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!
- Why do Businesses Exist Why does Starbucks Exist What Service does Starbucks Provide Really what is their product.
- The pattern of numbers below is an arithmetic sequence tex 14 24 34 44 54 ldots tex Which statement describes the recursive function used to..
- Morgan felt the need to streamline Edison Electric What changes did Morgan make.
Rewritten by : Barada
Final answer:
To find the distance the ship is from the port, calculate the northward and eastward components of its initial travel, add the subsequent eastward travel to the eastward component, and use the Pythagorean theorem to find the resultant distance.
Explanation:
Finding the Distance from the Port
To calculate how far the ship is from the port, we can use the Pythagorean theorem. Since the ship first travels at a bearing of 28° for 8.2 miles and then turns due east for another 4.3 miles, we can visualize this problem as a right-angled triangle where one leg is the path heading due east and the other leg is the path on a bearing of 28°.
1. We calculate the northward and eastward components of the 8.2 miles traveled on a 28° bearing:
- Northward Component = 8.2 miles * cos(28°)
- Eastward Component = 8.2 miles * sin(28°)
2. Since the ship also travels due east for 4.3 miles, this distance will be added to the eastward component from step 1.
3. The total eastward distance is the sum of the eastward component from step 1 and the 4.3 miles traveled due east.
4. The distance from the port can then be calculated using the Pythagorean theorem:
- Distance = √(Northward Component² + Total Eastward Distance²)
By applying these steps, we can find how far the ship is from the port.
