Question on Test: Hiker Displacement

In summary: Assuming the distances are small and the ground is level, it's a simple trigonometry problem to calculate the distances and angles.In summary, the hiker turned counter-clockwise from facing due south, then walked 450 meters in that direction before stopping. He then turned clockwise from facing due west, and walked 650 meters in that direction before stopping. He is now located 22⁰ East of South, 650 meters north of West.
  • #1
Anthony Gonzalez
1
0
Homework Statement
So I recently had a test, and spent practically the entire time on this one question, as I did not think that the question made sense. Maybe I should have skipped it, but nonetheless, I am confused. The question was something like this: "A hiker travels 450m, 22⁰ East of South. The hiker then turns and travels 650m, 37⁰ North of West. What is the hikers displacement?" So, I asked my teacher if the 650m North of West was where he ended at, but he said that the hiker just turns, and then travels in that direction. Does this question make sense?
Relevant Equations
Displacement
Distance
a
 
Physics news on Phys.org
  • #2
I think it makes sense. The phrases like "450m, 22⁰ East of South" and "650m North of West" are meant to be directions from where he is at the moment. You might interpret them some other way, but I think that would be unusual.
 
  • #3
Anthony Gonzalez said:
"A hiker travels 450m, 22⁰ East of South. The hiker then turns and travels 650m, 37⁰ North of West. What is the hikers displacement?"
To make this painfully explicit:

The hiker gets out his compass. It is marked with degrees.
He faces due south and then gently turns 22 degrees toward the east (i.e. counter-clockwise) from that facing. He does this turn in place without walking forward.
He then walks forward 450 meters in this direction and stops.

The hiker gets out his compass again.
This time he faces due west and then gently turns 37 degrees toward the north (i.e. clockwise) from that facing.
Again, he does this turn in place without walking forward.
He now walks 650 meters in this direction and stops.

How how far is he now from his original starting point?
In which direction is he now from his original starting point?
 
  • Love
Likes Delta2
  • #4
In a situation like this, where you're not certain about how to interpret the wording of a question, I suggest that you ask your instructor (during the test) to clarify it. In that case I (as the instructor) would have announced the clarification to the other people taking the test, so that they could all benefit from it equally.

If that is not possible, then I suggest that (as part of your solution) you indicate that you're not certain about the interpretation, draw a diagram that shows clearly how you interpreted it, and then base your calculations on that drawing. In that case I would have given you at least partial credit, depending on how reasonable I thought your interpretation was, depending in turn on what i know about your command of the English language.

Your instructor may be stricter than I would have been, but... "nothing ventured, nothing gained."
 
  • Like
Likes FactChecker and Delta2
  • #5
Assuming the hiker is traveling over level ground on Earth, and disregarding surface curvature because the distances are small, you can draw a solvable triangle given the information in the test question.

Presumably you already know that given 2 sides and their included angle you can construct the complete triangle. You're given 2 side lengths, but you're not directly given the included angle. The lengths of the sides, along with the 2 angles you're given relative to the cardinal points of the compass, which you already know are at 90° to their neighbors, are sufficient to construct the triangle.

Please remember that although "facing South" always means looking in the direction of somewhere in Antarctica, it does NOT mean that a person in Chicago who is facing South is facing in a direction parallel to the direction in which a person in New York who is facing South is facing.

Similarly, 2 persons at 60° N latitude and different longitudes both facing North form an isosceles triangle with their distance apart as the base and the North Pole as the altitude/vertex point.

You're given 2 sides, and 2 angles relative to cardinal points, and then you're asked to from that information calculate the distance, and the angle relative to a cardinal point, from the 2nd point to your point of origin.
 

What is "Hiker Displacement" on a test?

Hiker Displacement is a type of question that tests a person's understanding of distance and direction. It usually involves a hiker moving in a certain direction and the question asks for the final displacement or distance traveled.

How do you solve a "Hiker Displacement" question?

To solve a "Hiker Displacement" question, you will need to use concepts from physics and trigonometry. You will need to break down the displacement into its components and use the Pythagorean theorem to calculate the distance. You will also need to use trigonometric functions to determine the direction of the displacement.

What is the difference between displacement and distance in a "Hiker Displacement" question?

The displacement in a "Hiker Displacement" question refers to the shortest straight-line distance between the starting and ending points. The distance, on the other hand, refers to the actual distance traveled by the hiker, which may include changes in direction and detours.

What are some common mistakes when solving a "Hiker Displacement" question?

Some common mistakes when solving a "Hiker Displacement" question include forgetting to break down the displacement into its components, using the wrong trigonometric function, or forgetting to account for changes in direction. It is also important to pay attention to units and ensure they are consistent throughout the calculation.

How can I improve my skills in solving "Hiker Displacement" questions?

To improve your skills in solving "Hiker Displacement" questions, it is important to understand the fundamental concepts of physics and trigonometry. Practice using these concepts in different scenarios, and pay attention to units and calculations. It is also helpful to review your work and identify any mistakes to avoid them in the future.

Similar threads

  • Introductory Physics Homework Help
Replies
3
Views
364
  • Introductory Physics Homework Help
Replies
16
Views
340
  • Introductory Physics Homework Help
2
Replies
54
Views
2K
  • Introductory Physics Homework Help
Replies
6
Views
505
  • Introductory Physics Homework Help
Replies
6
Views
682
  • Introductory Physics Homework Help
Replies
12
Views
854
  • Introductory Physics Homework Help
Replies
3
Views
1K
  • Introductory Physics Homework Help
Replies
14
Views
1K
  • Introductory Physics Homework Help
Replies
2
Views
657
  • Introductory Physics Homework Help
Replies
8
Views
1K
Back
Top