Ship Displacement & Velocity | 8km to 15km

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In summary, the ship is initially 8km from the coast-line and the lighthouse has a bearing of N27E. After sailing for 30 minutes, the lighthouse is now 15km due north. Using the law of cosines, the displacement of the ship between the two recordings is 8.1km. However, the answer given in the book is 9.23km, which may be incorrect. Without knowing the initial direction of the ship, it is not possible to calculate the average velocity. Some possible interpretations of the problem may lead to different solutions.
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pivoxa15
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Homework Statement


A ship is 8km from a coast-line that stretches in an east-west direction. The navigator on the shop records that the lighthouse on the coast-line has a bearing of N27E. After sailing for 30 minutes the navigator records that the same lighthouse is 15km due north.

a) What is the displacement of the ship between the two recordings?
b) What is the average velocity of the ship?

Homework Equations


The Attempt at a Solution


I have attached a diagram. Is it correct?

If you do calculations from the diagram, you find that the original position was (0,8) and the new position is (4.08,15). So the displacement of the two recordings is (4.08,15)-(0,8)=(4.08,7). Which come down to an absolute length of 8.1km but the answers gave 9.23km as the absolute length. Where have I gone wrong. I can't do b) without knowing how to do a).

If I assume the hypotenues distance as 8km (in the triangle of 27 degrees) than I end up with (3.6,15)-(0,7.13)=(3.6,7.87) which gives an absolute length of 8.7km, which is still not right.
 

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  • #2
Are you sure 9.23 km is supposed to be the right answer? Are you sure you have all the values posted in your question correct? I think your answers are correct for each case based on the info you've given, if the problem is being interpreted correctly.
 
  • #3
I sure as hell can't get anything out of that problem. How do you know what direction the boat is initially sailing in?
 
  • #4
hage567 said:
Are you sure 9.23 km is supposed to be the right answer? Are you sure you have all the values posted in your question correct? I think your answers are correct for each case based on the info you've given, if the problem is being interpreted correctly.

That answer was posted at the back of the book. There is a small chance it's wrong. Maybe intepretation is an issue. But I can't intepret it in a way to get the answer they are looking for.
 
  • #5
I get a displacement of 8.1 using law of cosines where a=8/cos(27), b=15, and theta=27. I say book is wrong.
 
  • #6
denverdoc said:
I get a displacement of 8.1 using law of cosines where a=8/cos(27), b=15, and theta=27. I say book is wrong.

That's what I got as well so I agree with you.
 

Related to Ship Displacement & Velocity | 8km to 15km

1. What is ship displacement and how is it measured?

Ship displacement is the weight of water that is displaced by a ship, and it is typically measured in tons or metric tonnes. This measurement is taken by calculating the difference in water level before and after a ship enters the water.

2. How does ship displacement affect a ship's performance?

Ship displacement is directly related to a ship's buoyancy and stability. A ship with a larger displacement will have a greater buoyant force, allowing it to carry more weight. However, a larger displacement also means the ship will require more power to move through the water, which can affect its speed and fuel efficiency.

3. What is the significance of 8km to 15km in relation to ship displacement and velocity?

8km to 15km is a range that is often used to measure the velocity of a ship. This distance is typically used to calculate the ship's speed over a certain period of time, which can then be used to determine its average velocity.

4. How is ship velocity calculated?

Ship velocity is calculated by dividing the distance traveled by the time it takes for the ship to travel that distance. This can be measured in various units such as kilometers per hour, knots, or meters per second.

5. How do ship displacement and velocity affect each other?

Ship displacement and velocity are closely related. As mentioned before, a ship's displacement can affect its speed and fuel efficiency. In turn, a ship's velocity can also affect its displacement, as increased speed can cause a ship to displace more water as it moves through it.

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