iPhysics: Understanding displacement mathematically

The physics of displacement

As i previously stated in this topic "understanding displacement and differentiating it from distance", i explained displacement as the distance given with a specific direction, thus any distance given without a direction is not displacement.

see these instances:

John walked 20m towards east
The aeroplane flew 3000m in the north-east direction
The rocket flew vertically upwards and before 10 seconds, it was already 30,000km above
The lizard fell from the tower of pisa 3000km high but didn't break a bone.

Notice that all four examples, have displacement.

John walked 20m towards east

The aeroplane flew 3000m in the north-east direction

The rocket flew vertically upwards and before 10 seconds it was already 30,000km above

The lizard fell from the tower of Pisa 3,000 km high

Displacement as a vector is just targeting to tell how far a moving body is from its initial starting point

for instance:

If John walked 20m from point A to point B eastward,

John's displacement is 20m (because he is 20 metres away from A).

But if John walks back to A,

his displacement will become zero (because he is right back to his initial starting point) but his total distance travelled is actually 40 metres.

On another instance, let us assume that john on his way back to A, he decided to stop halfway (10m) at point C,

then at this point, john's displacement from point A is

"His displacement is 10m because that is just how far he is from his "initial" starting point A."

Another instance:

If James jogged round a football field in the manner showed in the diagram below starting from point "A",

can you be able to tell us his displacement from A ?

Ofcourse Yes!

His displacement is simply zero this is because he is right back to where he started.

But what if he stopped at C, will it still be so easy to find James displacement?

I wonder!

This case might assume the shape of a Goliath but trust me it is nothing close to that or even rocket science, it is super easy.

In solving this kind of problem there is one simple thing i want you to understand;

"displacement is a vector and you know what? vectors are not interested in long stories infact they find a way of making long stories short and simple."

Thus when a vector looks at this diagram this is what it does: It draws a straight line from A to C to form a right-angle-triangle and tries to finds the length of the new line.

using Pythagoras theorem

recall: the essence of displacement is to know the distance of a moving body away from its starting point.

Therefore if James's starting point is at A and his final position is at C then his (shortest) distance away from A which is his displacement is equal to 11.18 meters.

In thesame sense, if James's final position were to be at D