Man goes 50 m to North , then 40 m to East and 20 due South. We need to find out the displacement of the whole journey.
Displacement is the shortest length between the starting and stopping point. It's a vector having both directions and magnitude.
Look.at the attached diagram to understand his trajectory from home to field.
So the diagram shows a Trapezium like figure which is formed in his journey . We need to find x.
Thos can be done using Pythagoras theorem:
Given:-
To find:-
Solution:-
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Answer:
Man goes 50 m to North , then 40 m to East and 20 due South. We need to find out the displacement of the whole journey.
First of all , we need to define Displacement :
Displacement is the shortest length between the starting and stopping point. It's a vector having both directions and magnitude.
Look.at the attached diagram to understand his trajectory from home to field.
So the diagram shows a Trapezium like figure which is formed in his journey . We need to find x.
Thos can be done using Pythagoras theorem:
So displacement is 50 m
Given:-
To find:-
Solution:-
♦![\texttt{Distance travelled towards North is AB.}\\ ></p><p>♦ <img src=](https://tex.z-dn.net/?f=%5Ctexttt%7BDistance%20travelled%20towards%20North%20is%20AB.%7D%5C%5C)
♦![\texttt{Distance travelled towards South is CD.} \texttt{Distance travelled towards South is CD.}](https://tex.z-dn.net/?f=%5Ctexttt%7BDistance%20travelled%20towards%20South%20is%20CD.%7D)
•![\texttt{DF = BC, as BCDF forms a rectangle.} \texttt{DF = BC, as BCDF forms a rectangle.}](https://tex.z-dn.net/?f=%5Ctexttt%7BDF%20%3D%20BC%2C%20as%20BCDF%20forms%20a%20rectangle.%7D)
•![\texttt{Then CD = BF = 20 m.} \texttt{Then CD = BF = 20 m.}](https://tex.z-dn.net/?f=%5Ctexttt%7BThen%20CD%20%3D%20BF%20%3D%2020%20m.%7D)
∴![\bold{\underline{So,\ the\ displacement\ of\ the\ man\ is\ 50\ m\ from\ his\ house\ to\ the\ field.}} \bold{\underline{So,\ the\ displacement\ of\ the\ man\ is\ 50\ m\ from\ his\ house\ to\ the\ field.}}](https://tex.z-dn.net/?f=%5Cbold%7B%5Cunderline%7BSo%2C%5C%20the%5C%20displacement%5C%20of%5C%20the%5C%20man%5C%20is%5C%2050%5C%20m%5C%20from%5C%20his%5C%20house%5C%20to%5C%20the%5C%20field.%7D%7D)