Question

A person moves 10m south and then 10m towards east and finally 10√2m in north-west direction.The displacement of the person for the entire journey is:

Answer 1

Hey there !

Given , A person moves 10m south and then 10m towards east and finally  10√2m in north-west direction.

So,

Displacement is the shortest line  segment joining Initial and Final points .

Now , CONSIDERING THE FIRST TWO CASES ,

⇒ 10m south and then 10m towards east

They would form a right angled triangle if joined .

Hypotenuse would be equal to root of the sum of squares of sides

$h =\sqrt{x^{2}+y^{2} }$

here , x = 10 m , y =10 m

$h =\sqrt{10^2+10^2} \\ \\ h =\sqrt{100 +100} \\ \\ h =\sqrt{200} \\ \\ h = 10\sqrt{2}$

So , The man moved along the diagonal and reached his starting point again .

His displacement is 0 .

The displacement of the person for the entire journey is 0m

Answer 2

Given A person moves 10m south and then 10m towards east and finally 10√2m in north-west direction.The displacement of the person for the entire journey is

When we draw a diagram of the directions the person is moving we get a right angled triangle.

We need to find the displacement which is change in direction or position.

So by Pythagoras theorem we have AC ^2 = AB^2 + BC^2, the square on the hypotenuse is equal to the sum of the square on the other two sides.

      AC^2 = 10^2 + 10^2

       AC = √100 + 100

       AC = √200

AC = 10√2

The displacement is 10√2 - 10√2 = 0

Since he comes to the same position the displacement is zero,