A certain corner of a room is selected as the origin of a rectangular coordinate system. If an insect is sitting on an adjacent wall at a point having coordinates (2,1), where the units are in metres, what is the distance of the insect from this corner of the room?

(Ans: 2.2m)


Given:

Point having coordinates  (2, 1)


To Find:

Distance between the point and given corner of the room = r = ?


Solution: 

Let the given corner coordinate be the origin (0, 0) of the coordinate system then the position vector of the given point will be 

`\vec {r}` = (x₂ - x₁)`\hat {i}` - (y₂ - y₁)`\hat {j}` 

by putting values [from origin Coordinate x₁ = 0,  y₁ = 0, and Point coordinate are x₂ = 2,  y₂ = 1,

`\vec {r}` = (2 - 0)`\hat {i}` + (1 - 0)`\hat {j}`

`\vec {r}` = 2 `\hat {i}` + 1 `\hat {j}`

Here x-component = 2 and y-component = 1

The magnitude of the position vector `\vec {r}` will be its length, which is the distance between the two given points and the origin. So, by using the formula 

|`\vec {r}`| = `\sqrt {x^2 + y^2}`

by putting values 

r = `\sqrt {2^2 + 1^2}`

r = `\sqrt {4 + 1}`

r = `\sqrt {5}`

r = 2.2 metres  ------Ans
Thus the distance between the points (2, 1) and corner (0, 0)   is 2.2 metres.


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Numerical Problem 2.2
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List of 11th Physics Numerical Problems of Chapter - 2
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