Question

A man walks 4m east ,then 5m north,then taking a right turn walks 8m straight.Calculate the distance travelled by the man and its displacement.

Answer 1

distance is 4m + 5m + 8m = 17m
can u please check the question I think its 8m turning left

Answer 2

DISTANCE IS 17 m & DISPLACEMENT IS 13 m.

Given:

• Man walks 4 m east, 5 m north and then turns right (i.e. east) and walks 8 m.

To find:

• Distance & Displacement ?

Calculation:

Distance is the total path length travelled.

$distance = 4 + 5 + 8 = 17 \: m$

However, displacement is the shortest length between the starting and stopping point of the object.

Let displacement vector be $\vec{d}$

• Towards East means $\hat{i}$
• Towards North means $\hat{j}$

$\vec{d} = 4 \hat{i} + 5 \hat{j} + 8 \hat{i}$

$\implies\vec{d} = 12 \hat{i} + 5 \hat{j}$

$\implies | \vec{d}| = \sqrt{ {12}^{2} + {5}^{2} }$

$\implies | \vec{d}| = \sqrt{144 + 25}$

$\implies | \vec{d}| = \sqrt{169}$

$\implies | \vec{d}| =13 \: m$

So, displacement is 13 m & distance is 17 m.