A boy moves 4 m to the east then he turned left and moves 12 m, after that he climbs a pole to a height of 3 m. Find the displacement of the boy.

CONCEPT:

Distance:

• The measurement of how much any object moved is called distance.
• It is a scalar quantity.

Displacement

• It is the shortest distance between the initial and final positions of the particle.
• It is a vector quantity.

CALCULATION:

Let the initial position of the boy is considered as the origin.

So the initial position vector of the boy is,

\(⇒ \vec{d_{1}}=0\hat{i}+0\hat{j}+0\hat{k}\)     -----(1)

So according to the diagram, the final position vector of the boy is given as,

\(⇒ \vec{d_{2}}=4\hat{i}+3\hat{j}+12\hat{k}\)     -----(2)

By equation 1 and 2 the resultant displacement of the boy is given as,

\(⇒ d=\sqrt{\left [ \left ( x_{2}-x_{1} \right )^2 +\left ( y_{2}-y_{1} \right )^2 +\left ( z_{2}-z_{1} \right )^2 \right ]}\)

\(⇒ d=\sqrt{\left [ \left ( 4-0 \right )^2 +\left ( 3-0 \right )^2 +\left ( 12-0 \right )^2 \right ]}\)

⇒ d = 13 m

• Hence, option 1 is correct.

• The magnitude of displacement is equal to the minimum possible distance between two positions. So distance ≥ Displacement.
• For a moving particle, distance can never be negative or zero while displacement can be (Zero displacement means that body after motion has come back to initial position). i.e., Distance > 0 but Displacement > = or < 0.
• For motion between two points displacement is single-valued while distance depends on the actual path and so can have many values.
• For a moving particle, distance can never decrease with time while displacement can.
• A decrease in displacement with time means the body is moving towards the initial position.