In what direction is the scout's position relative to the campsite?

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SUMMARY

The discussion focuses on a scout's movement and position relative to a campsite after a series of directional walks. The scout first walks 5 km east, then turns left to walk 4.5 km along a circular arc centered at the campsite, and finally walks 3 km directly towards the camp. The key questions include determining the scout's final distance from the camp, the direction of his position relative to the campsite in degrees clockwise from north, and the ratio of the final displacement to the total distance walked.

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  • Understanding of vector displacement and direction
  • Knowledge of circular motion and arc length
  • Familiarity with basic trigonometry and geometry
  • Ability to analyze motion with constant acceleration
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  • Calculate the scout's final distance from the campsite using the Pythagorean theorem
  • Determine the angle of the scout's position using trigonometric functions
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  • Study the equations of motion for particles under constant acceleration
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Okay, the first one I have no clue how to set up or start, so a hunt would be nice. The second one, I figured out (a) but can''t seem to get (b) or (c) and want to know what I'm doing wrong.

Homework Statement


A scout walks 5 km due east from camp, then turns left and walks 4.5 km along the arc of a circle centered at the campsite, and finally walks 3 km directly toward the camp.
(a) How far is the scout from camp at the end of his walk?
___ km

(b) In what direction is the scout's position relative to the campsite?
___ ° (clockwise from north)

(c) What is the ratio of the final magnitude of the displacement to the total distance walked?
___





A particle moves in the xy plane with constant acceleration. At time zero, the particle is at x = 3.0 m, y = 6.0 m, and has velocity v = 1.0 m/s i + 7.0 m/s j. The acceleration is given by the vector a = 9.0 m/s i + -1 m/s j.


What is the velocity vector at t=3.0s
I got (28 m/s) i+ (4 m/s) j

What is the position vector at t=5.0s

What is the magnitude and direction of the position vector

Homework Equations





The Attempt at a Solution

 
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I would start with a diagram!
For the circle part, you know the distance from camp will be the same everywhere on the circle so that part is easy. You can get the angle through figuring out what part of the full circumference is walked, and take that same part of 360 degrees.
 

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