Measuring Distance with Vectors: Tips and Tricks for Physics Students"

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SUMMARY

The discussion focuses on devising a method to measure the distance from a physics laboratory to an external feature using only a protractor, meter stick, and vector diagram. The proposed approach involves measuring the angle to the top of the object from two different points: next to the window and 1 meter away from the window. This method leverages trigonometric principles to create a right triangle, allowing for the calculation of distance without leaving the building. The accuracy of this method is estimated to be within 10% for distances less than half a mile.

PREREQUISITES
  • Understanding of basic trigonometry and right triangles
  • Familiarity with vector diagrams and their applications
  • Ability to use a protractor for angle measurement
  • Knowledge of scale drawing techniques
NEXT STEPS
  • Research the principles of triangulation for distance measurement
  • Learn how to construct and interpret vector diagrams
  • Study the application of trigonometric functions in real-world scenarios
  • Explore methods for improving measurement accuracy in physics experiments
USEFUL FOR

Physics students, educators, and anyone interested in practical applications of trigonometry and vector analysis in distance measurement.

frogger20027
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The problem reads:
"See if you can devise a METHOD (not a numerical answer) of measuring the distance from your physics laboratory to some outside feature (flag-pole, church steeple, etc.) WITHOUT leaving the building. If the object is less than a half-mile distant the job can be done within about 10%, using ONLY a protractor, meter stick, and drawing a vector diagram to scale."

I understand vectors and all, and I understand what the question is asking. I've tried working out trig functions on paper (since this is a right triangle in which you can measure the angle from the ground to the top of the "outside feature"), but there are just too many unknown variables to actually come up with an equation or relationship among them.

I would much appreciate any suggestions or assistance!
 
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What if you measured the angle to the top of the object from next to the window and then 1 meter away from the window?
 

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