Calculating Displacement Vectors: Solving Problems in St. Louis and at Sea

In summary, the conversation discusses two physics problems and provides instructions on how to solve them. The first problem involves determining the distance to the base of the Gateway-to-the-West arch in St. Louis, Missouri, given the height of the arch and the angle of line of sight. The second problem involves calculating the components of a ship's displacement vector in different directions. The expert advises using trigonometry to solve both problems and clarifies that the first problem can be solved using the tangent function and the second problem can be solved using the sine and cosine functions. The conversation also provides additional information about the height of the arch and advises assuming a right triangle for these types of problems unless otherwise stated.
  • #1
taylor89
4
0
Hi, I am new here and I am taking Ap Physic I have some problems and I can't figure them out I posted them below. Any help would be appriciated...:smile:

You are driving into St. Louis, Missouri, and in the distance you see the famous Gateway-to-the-West arch. This monument rises to a height of 192 m. You estimate your line of sight with the top of the arch to be 7.8° above the horizontal. Approximately how far (in kilometers) are you from the base of the arch?_____km

An ocean liner leaves New York City and travels 47.0° north of east for 218 km. How far east and how far north has it gone? In other words, what are the magnitudes of the components of the ship's displacement vector in the following directions?
(a) due east ______km
(b) due north______km
 
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  • #2
Hi, Tarylor. Welcome the forum.
You have to show us what you have done before asking for help. Both the answers require nothing more than simple trigonometry.
 
  • #3
I don't really know how to show you what I've done cause it is a drawing I just need instructions on how to solve
 
  • #4
For the first, use the definition of the tangent of an angle. The second requires to use the sine and cosine functions.
 
  • #5
K

K I got this one can you help me with this one.

You are driving into St. Louis, Missouri, and in the distance you see the famous Gateway-to-the-West arch. This monument rises to a height of 192 m. You estimate your line of sight with the top of the arch to be 7.8° above the horizontal. Approximately how far (in kilometers) are you from the base of the arch? _______km
 
  • #6
I assume that you have drawn the appropriate diagram for this problem. Do you know that the ratio between the height of the monument and your distance to it is?
 
  • #7
actually i was unsure if this looked like a right triangle or if it had an arc
 
  • #8
For problems such as these, you can safely assume that it's a right triangle, unless otherwise mentioned, of course.
 
  • #9
You can now use the tangent of the angle above the horizontal to calculate the required distance. I've checked in the internet and the arc's height is 630 feet.
 
  • #10
Btw, the height of the arch is 192 metres, not Km.
 
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FAQ: Calculating Displacement Vectors: Solving Problems in St. Louis and at Sea

1. What is a ship's displacement vector?

A ship's displacement vector is a mathematical representation of the ship's movement through water. It takes into account the magnitude and direction of the ship's movement and is typically measured in meters.

2. How is a ship's displacement vector calculated?

A ship's displacement vector is calculated using the ship's speed, heading, and water currents. This data is combined using vector addition to determine the overall displacement vector.

3. Why is a ship's displacement vector important?

A ship's displacement vector is important for navigation and tracking purposes. It allows for accurate tracking of a ship's movement, which is essential for safety and efficiency at sea.

4. How does a ship's displacement vector differ from its velocity vector?

A ship's displacement vector represents the distance traveled by the ship, while its velocity vector represents the rate at which the ship is moving. The displacement vector is a scalar quantity, while the velocity vector is a vector quantity that includes direction.

5. Can a ship's displacement vector change over time?

Yes, a ship's displacement vector can change over time as the ship's speed and heading change. Water currents and other external factors can also affect the ship's displacement vector.

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