Calculating Displacement Using Vectors and Angles

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SUMMARY

The discussion focuses on calculating the displacement of a roller coaster that moves 85 meters horizontally and then 45 meters at an angle of 30 degrees above the horizontal. The correct direction for the angle is northeast, which corresponds to a 30-degree angle from the horizontal axis. To find the total displacement, one must visualize the problem as a right triangle and apply vector addition principles to determine the resultant displacement from the starting point.

PREREQUISITES
  • Understanding of basic trigonometry, specifically sine and cosine functions.
  • Familiarity with vector addition and graphical representation of vectors.
  • Knowledge of right triangle properties and Pythagorean theorem.
  • Ability to interpret angles in standard position on a coordinate plane.
NEXT STEPS
  • Learn how to apply the Pythagorean theorem to calculate resultant vectors.
  • Study trigonometric functions to resolve vectors into their components.
  • Explore graphical methods for vector addition and displacement visualization.
  • Investigate real-world applications of vector calculations in physics and engineering.
USEFUL FOR

Students studying physics or mathematics, educators teaching vector concepts, and anyone interested in solving real-world problems involving displacement and angles.

jubbly
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Hey guys I'm lost with this word problem.
A roller coaster moves 85m horizontally, then travels 45m at an angel of 30.0° above the horizontal. What is its displacement from its starting point?

I started out by drawing a 85m line. But now I'm confused because I have to set a 30 degree angle. Would I draw a line to the northeast or northwest?

That's all the need I'll need for now. Thanks guys!
 
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jubbly said:
I have to set a 30 degree angle. Would I draw a line to the northeast or northwest?

You would draw it NorthEast, or 3 o'clock angle, or 30 degrees, or Up-Right, etc. From there, you can find the total displacement from starting point (assuming you can see the triangle).
 

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