Question

an ant travels a distance of 12cm from AtoB and then moves a distance of 9cm at right angle to AB. find the resultant displacement and the total distance covered by it.

Answer 1

Total distance travelled by ant=12+9=21 cm
Total displacement=√12²+9²=
                              =√225
                              =15 cm 

Answer 2

Concept:

A displacement is a vector whose length is the shortest distance from the initial to the final position of an object or point in motion.

Given:

An ant travels $12cm$ from $A$ to $B$ and then moves $9cm$ at a right angle to $AB$.

Find:

The resultant displacement and the total distance covered by the ant.

Solution:

From point $A$ to $B$, the distance is $12cm$ and the distance from the right angle is $9cm$ to a point $C$.

By joining, $AC$ we obtain a right-angled triangle where $AC$ is the displacement.

Using Pythagoras theorem,

$AC=\sqrt{AB^2+BC^2}\\AC=\sqrt{12^2+9^2}\\AC=\sqrt{144+81}\\AC=\sqrt{225}\\AC=15cm$

And, the total distance covered by the ant is $12cm+9cm=21cm$.

The resultant displacement and the total distance covered by the ant are $15cm$ and $21cm$ respectively.

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