Vector clock and vector dog displacement problems

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SUMMARY

The discussion focuses on calculating the displacement vectors for two problems: the minute hand of a watch and a dog's movement. For the minute hand, the x and y components of the displacement vector from 8:00 AM to 8:20 AM are derived using trigonometric principles, resulting in a total displacement of 2.8 cm. For Sparky the dog, the net displacement involves calculating the x and y components based on his movements northeast, west, and south, ultimately requiring the application of the Pythagorean theorem to find the magnitude of the net displacement.

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  • Understanding of trigonometric functions for vector resolution
  • Familiarity with the Pythagorean theorem
  • Basic knowledge of coordinate systems
  • Ability to visualize geometric representations of vectors
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  • Study the application of the Pythagorean theorem in vector calculations
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Homework Statement


The minute hand on a watch is 2.00 cm in length. What is the length (in cm) of the i hat component of the displacement vector of the tip of the minute hand from 8:00 AM to 8:20 AM? What is the length (in cm) of the j hat component of the displacement vector of the tip of the minute hand from 8:00 AM to 8:20 AM?

Homework Equations



A^2 + B^2 = C^2

The Attempt at a Solution



I'm having trouble trying to find a geometric way of viewing the problem.
/\
l This is how I'm viewing 8:00 to 8:20 AM with only the minute hand.
l 2 cm
l
\
\ 2 cm
\
>

What I'm trying to figure out in the problem is what are the x and y components. My attempt is this:

x component
/\----
l l
l l
l l y component
\ l
\ l
\ l
>

I know from the tip of the minute hand at 8:00 AM to 8:20 AM is 2.8 cm, (2^2 + 2^2 = C^2, C = 2.8 cm)

Homework Statement


Jill's dog Sparky runs 70.0 m northeast to a tree, then 30.0 m west to a second tree, and finally 90.0 south to a third tree. Draw a picture and establish a coordinate system. Calculate the x component (in m) of Sparky's net displacement.
Calculate the y component (in m) of Sparky's net displacement.
Calculate the magnitude (in m) of Sparky's net displacement

Homework Equations



A^2 + B^2 = C^2

The Attempt at a Solution



For this problem, I'm again having trouble setting up values to put into an equation and viewing what in a picture is the x and y components. Here is a picture of how I'm attempting to view the problem with a coordinate system.

/\
l 30 m
-- l--------/
l l /
l 76.2 m l /
l l / 70.0 m
90 m l l /
l l /
<-------------------- l -------------------->
l l
l l
l l
l l
-- l
l
l
l
\/

Much thanks,
Daniel
 
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Actually I'm clueless on putting the drawings I had for the problems into html so disregard the attempted pictures.
 
Last edited:
I can't make out your figure. But, how about using the angle made by the minute hand, and some trig, in order to get the x and y components of the hand's tip at the times listed (8:00 and 8:20)?
 

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