Vector magnitude and displacement

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Homework Help Overview

The problem involves calculating the total displacement of a car that travels in multiple directions, specifically east, north, and at an angle east of north. The context is rooted in vector analysis and requires understanding of vector components and magnitudes.

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants discuss the need to include all segments of the journey in the vector diagram, particularly the contribution of the 28 km segment. There are questions about how to break down this segment into its components and how to combine these with the other distances traveled.

Discussion Status

Participants are actively engaging with the problem, suggesting methods to resolve the components of the vectors and discussing the implications of their calculations. There is a focus on ensuring all parts of the journey are accounted for, and some guidance has been provided regarding the breakdown of the 28 km segment.

Contextual Notes

There is an emphasis on understanding the meaning behind the calculations rather than just applying formulas. Participants are encouraged to visualize the problem through diagrams, which may aid in clarifying the contributions of each segment to the overall displacement.

jpd5184
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Homework Statement



A car is driven east for a distance of 48 km, then north for 25 km, and then in a direction 25° east of north for 28 km. Draw the vector diagram and determine the total displacement of the car from its starting point.

whats the magnitude and direction(counterclockwise from east)


Homework Equations



A^2=Ax^2 + Ay^2


The Attempt at a Solution



i plugged in 48km for Ax and 25km for Ax and got 82.103km for my answer
 
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you seem to be missing the contributions of the 28 km. Draw the diagram and attach it.
 
i noticed that the 28km was left out, i drew it on my picture but I am not sure what forumula to use to utilize it.
 
Are you able to break down the 28 km into its east and north components? If you can do that, then add all the east components together, and then ... can you do it now?
 
do you mean like:

x= 28cos25
y= 28cos65
 
yes, except I think your angles should be interchanged. Then to get the overall displacement you have an x component of 48+28sin25 and a y component of ... Then use pythagoras on the two overall components. In future, try to not think of 'plugging into a formula' without thinking what it means.
 

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