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Question on my test that I thought didn't make sense (hiker's total walking displacement)

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?
Homework Equations
Displacement
Distance
a
 

FactChecker

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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.
 

jbriggs444

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"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?
 

jtbell

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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."
 
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Assuming the hiker is travelling 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.
 

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