Question

Find the displacement $OD$ in the following figure

Answer 1

In this question, we have to calculate the displacement of a point i.e. the difference between the initial point and the final point. Here, we make use of properties of the rectangle, distance and displacement concept and Pythagoras theorem.

Complete step by step answer:
Let us consider an object is displacing from point $D$to point $O$via points $A,B,C$.

Extending the point $D$ to touch seg $OA$ at $P$. Also extend point $D$to touch seg $AB$ at $Q$.Join the points $OD$. We have to find this displacement $OD$. From the figure, Using the properties of rectangle that opposite sides are equal and all angles are right angled triangle, we have
$BC = QD = AP = 4$ km
$\Rightarrow AQ = 3$ km and $QB = 1$ km
So, we get,
$OP = 4$ km and $PD = 3$ km -------------$(1)$
Now, consider the triangle $\Delta OPD$, It is a right angled triangle at $\angle P$
So, by using Pythagoras theorem,
$O{D^2} = O{P^2} + P{D^2}$
Substituting the values from eq$(1)$ , we get
$O{D^2} = {4^2} + {3^2}$
$\Rightarrow O{D^2} = 16 + 9 = 25$
Taking square root, we get
$\therefore OD = 5$ km

Hence, the displacement $OD = 5$ km.

Note: Displacement and distance are different terms having different meanings.Displacement is the difference between the initial and final position of the object and distance is the length of path covered by the object in a given time interval. Also, displacement is a vector quantity and distance is a scalar quantity.