A man travels a distance of $ 1.5 \mathrm{~m} $ towards east, then $ 2.0 \mathrm{~m} $ in south and then $ 4.5 \mathrm{~m} $ towards east. Find the total distance travelled? Find the resultant displacement?

Distance refers to how far an object has travelled in total (It has only magnitude, no direction).

So, the total distance travelled by the man will be = 1.5 + 2.0 + 4.5 = 8m.

Displacement is nothing more than a change in position (It has magnitude as well as direction). It is the shortest distance between from the initial position to the final position.

According to the question, the man travelled 1.5m and 4.5m in the east direction, and, only 2.0m in the south direction. Therefore, we can directly make a diagram for 6m east and 2m south, the resultant will be same.

Here, we use the resultant displacement formula when units of distance are used to specify the initial and final location. 

The resultant displacement formula is written as: $S=\sqrt{{x}^{2}+{y}^{2}}$.

Where 'S' stands for displacement. X is the first direction that the object is travelling (6m east) and Y is the second direction that the object is travelling (2m south). 

Now, substituting the values in the formula we get-

$S=\sqrt{{6}^{2}+{2}^{2}}$

$S=\sqrt{36+4}$

$S=\sqrt{40}$

$S=2\sqrt{10}$

Hence, the resultant displacement will be $2\sqrt{10}$.

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Updated on: 10-Oct-2022

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