CBSE Class 12-science Answered
A particle suffers 3 displacements by 4m in the northward,2m in the south-east and 2m in the south-west directions.
What is the displacement of the particle?
Asked by kandappan | 19 Apr, 2020, 08:37: AM
![](https://images.topperlearning.com/topper/tinymce/imagemanager/files/f629a12f1812f358943eee0a40ca230d5e9bf6b76c63c1.96476822vvv.png)
Let us consider X-Y coordinate system so that X-axis in West-to-East direction and
Y-axis in South-to-North direction as shown in figure.
Let us assume initially the particle is at origin O.
First displacement to point A is 4m north, i.e. 4
m , where
is a unit vector in y-direction.
![begin mathsize 14px style j with hat on top end style](https://images.topperlearning.com/topper/tinymce/cache/ef647306fae7d3b52276fc8b581df5b6.png)
![begin mathsize 14px style j with hat on top end style](https://images.topperlearning.com/topper/tinymce/cache/ef647306fae7d3b52276fc8b581df5b6.png)
Position vector of point A = 4
m
![begin mathsize 14px style j with hat on top end style](https://images.topperlearning.com/topper/tinymce/cache/ef647306fae7d3b52276fc8b581df5b6.png)
Second displacement is 2 m in the direction South-East to the point B .Hence displacement = √2
- √2 ![begin mathsize 14px style j with hat on top end style](https://images.topperlearning.com/topper/tinymce/cache/ef647306fae7d3b52276fc8b581df5b6.png)
![begin mathsize 14px style i with hat on top end style](https://images.topperlearning.com/topper/tinymce/cache/a5a79159fc1a127cc872f245943c4834.png)
![begin mathsize 14px style j with hat on top end style](https://images.topperlearning.com/topper/tinymce/cache/ef647306fae7d3b52276fc8b581df5b6.png)
Hence position vector of B = ( 4
) + ( √2
- √2
) = √2
+ ( 4 - √2 ) ![begin mathsize 14px style j with hat on top end style](https://images.topperlearning.com/topper/tinymce/cache/ef647306fae7d3b52276fc8b581df5b6.png)
![begin mathsize 14px style j with hat on top end style](https://images.topperlearning.com/topper/tinymce/cache/ef647306fae7d3b52276fc8b581df5b6.png)
![begin mathsize 14px style i with hat on top end style](https://images.topperlearning.com/topper/tinymce/cache/a5a79159fc1a127cc872f245943c4834.png)
![begin mathsize 14px style j with hat on top end style](https://images.topperlearning.com/topper/tinymce/cache/ef647306fae7d3b52276fc8b581df5b6.png)
![begin mathsize 14px style i with hat on top end style](https://images.topperlearning.com/topper/tinymce/cache/a5a79159fc1a127cc872f245943c4834.png)
![begin mathsize 14px style j with hat on top end style](https://images.topperlearning.com/topper/tinymce/cache/ef647306fae7d3b52276fc8b581df5b6.png)
Third displacement is 2 m in the direction south west to the point C .Hence displacement = -√2
- √2 ![begin mathsize 14px style j with hat on top end style](https://images.topperlearning.com/topper/tinymce/cache/ef647306fae7d3b52276fc8b581df5b6.png)
![begin mathsize 14px style i with hat on top end style](https://images.topperlearning.com/topper/tinymce/cache/a5a79159fc1a127cc872f245943c4834.png)
![begin mathsize 14px style j with hat on top end style](https://images.topperlearning.com/topper/tinymce/cache/ef647306fae7d3b52276fc8b581df5b6.png)
Hence position vector of C = ( √2
+ ( 4 - √2 )
) + ( -√2
- √2
) = ( 4 - 2√2 )
= 1.172 ![begin mathsize 14px style j with hat on top end style](https://images.topperlearning.com/topper/tinymce/cache/ef647306fae7d3b52276fc8b581df5b6.png)
![begin mathsize 14px style i with hat on top end style](https://images.topperlearning.com/topper/tinymce/cache/a5a79159fc1a127cc872f245943c4834.png)
![begin mathsize 14px style j with hat on top end style](https://images.topperlearning.com/topper/tinymce/cache/ef647306fae7d3b52276fc8b581df5b6.png)
![begin mathsize 14px style i with hat on top end style](https://images.topperlearning.com/topper/tinymce/cache/a5a79159fc1a127cc872f245943c4834.png)
![begin mathsize 14px style j with hat on top end style](https://images.topperlearning.com/topper/tinymce/cache/ef647306fae7d3b52276fc8b581df5b6.png)
![begin mathsize 14px style j with hat on top end style](https://images.topperlearning.com/topper/tinymce/cache/ef647306fae7d3b52276fc8b581df5b6.png)
![begin mathsize 14px style j with hat on top end style](https://images.topperlearning.com/topper/tinymce/cache/ef647306fae7d3b52276fc8b581df5b6.png)
Hence net displacement = 1.172 ![begin mathsize 14px style j with hat on top end style](https://images.topperlearning.com/topper/tinymce/cache/ef647306fae7d3b52276fc8b581df5b6.png)
![begin mathsize 14px style j with hat on top end style](https://images.topperlearning.com/topper/tinymce/cache/ef647306fae7d3b52276fc8b581df5b6.png)
Answered by Thiyagarajan K | 19 Apr, 2020, 12:52: PM
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