Vector clock and vector dog displacement problems

AI Thread Summary
The discussion revolves around calculating displacement vectors for two problems: the minute hand of a watch and a dog's movement. For the minute hand, the user seeks to determine the x and y components of its displacement from 8:00 AM to 8:20 AM, suggesting the use of trigonometry to find these components. In the second problem, the user is trying to calculate the net displacement of a dog that moves in multiple directions, also struggling with visualizing the x and y components. The discussion emphasizes the need for geometric interpretation and the application of trigonometric principles to solve these vector problems effectively. Overall, both problems highlight the importance of breaking down movements into their respective components for accurate 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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