Magnitude and direction of displacement

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SUMMARY

The discussion focuses on calculating the magnitude and direction of displacement for a man walking 32.5 km at 45° north of east, followed by 17.0 km due east. The solution involves breaking down the movements into X and Y components, applying Pythagorean theorem to find the resultant magnitude, and using trigonometric functions to determine the angle. The resultant angle is confirmed to be in quadrant I, adhering to the CAST rule for angle measurement.

PREREQUISITES
  • Vector addition principles
  • Trigonometric functions (sine, cosine, tangent)
  • Pythagorean theorem
  • Understanding of coordinate quadrants and the CAST rule
NEXT STEPS
  • Practice vector addition with different angles and magnitudes
  • Explore advanced trigonometric applications in physics
  • Learn about vector components in two-dimensional motion
  • Study the implications of displacement in real-world scenarios
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Students studying physics, particularly those focusing on mechanics and vector analysis, as well as educators looking for practical examples of vector addition.

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Homework Statement



Determine the magnitude and direction of the displacement if a man walks 32.5 km 45° north of east, and then walks due east 17.0 km.
 
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Use basic vector addition. Then write the resultant as an angle and magnitude
 
A good practice to develop is using components. It takes longer for these sorts of easy problems, but if you nail down the method now it'll really help once you get to more complicated stuff.

Things to remember:

45o North of East basically means 45o North measured from the East.

So just split them into X and Y components and add. Then just use pythagoras to get the magnitude, and some basic trig: tan\Theta= y/x to get the angle.
Remember the angle is always measured from the closest X axis. If you remember the CAST rule you can figure out what quadrant the angle is in.

For this one it should end up in quadrant I.

Have a go at it.
 

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