Question

The dimensions (measurements) of a hall are $12m,4m,and3m$, respectively. An ant starts at one corner of the hall, travels only along the edges, and reaches a diagonally opposite corner, taking the shortest possible route. Find the distance traveled by the ant and its magnitude of displacement.

Answer 1

Step 1: Given data:

Dimensions of room are:

1. $l=12m$
2. $b=4m$
3. $h=3m$

The diagrammatic representation of the given data is given below:

Step 2: Calculate the total distance:

Distance moved by the ant = $l+b+h$

$$\begin{gathered} Dis\tan ce=12+4+3 \\ Dis\tan ce=\mathbf{19}\mathit{m} \end{gathered}$$

Step 3: Calculate the displacement:

Displacement of the ant, from one corner to a diagonally opposite corner is equal to the length of the diagonal.

$$\begin{gathered} Displacement=\sqrt{l^2+b^2+h^2} \\ Displacement=\sqrt{{12}^2+4^2+3^2} \\ Displacement=\sqrt{144+16+9} \\ Displacement=\sqrt{169}=\mathbf{13}\mathit{m} \end{gathered}$$

Therefore,

The distance traveled by the ant is $\mathbf{19}\mathit{m}$ and the displacement of the ant is $\mathbf{13}\mathit{m}$.