Question

An ant climbs up five stairs, each of width 20cm and height 20cm. Find the distance covered and displacement of the ant.

Answer 1

Hint: Distance travelled by a body is equal to the total length that the body covered during its motion. If the ant climbs up on step, it will cover a distance equal to the sum of the lengths of the width and the height of the step. For displacement find the final position of the ant and use distance formula between two points.

Complete step by step answer:
Distance travelled by a body is equal to the total length that the body covered during its motion. It is given that the ant climbs up five steps and the width and height of each step are equal to 20 cm and 20 cm respectively. This means that if the ant climbs up on step, it will cover a distance equal to the sum of the lengths of the width and the height of the step.Therefore, the distance covered by the ant when it climbs up one step is equal to $20cm+20cm=40cm$.

Similarly, when the ant climbs up five such steps, the total distance covered by it is equal to $5\times 40cm=200cm$. The magnitude of displacement is equal to the line segment joining the final position and the initial position of the body. In this case, let us consider the initial point of the ant to be the origin of the Cartesian plane with the vertical as y-axis and the horizontal as x-axis.

Then this means that when the ant climbs up five steps, it will be displaced by $5\times 20=100cm$ along both the axes. This is because the width and height of each step is equal to 20cm.Therefore, the final position of the ant is (100cm,100cm). We know that the initial position is (0,0). Now, use distance formula to find the length (d) of the line segment joining the initial and the final points.
$\Rightarrow d=\sqrt{{{(100-0)}^{2}}+{{(100-0)}^{2}}}\\
\therefore d =100\sqrt{2}cm$

Therefore, the displacement of the ant is equal to $100\sqrt{2}cm$.

Note: Distance and displacement are two similar but different quantities. As said above, distance is the total length covered by the body and displacement is the length joining the final and the initial positions of the body. Distance is a scalar quantity and displacement is a vector quantity.We can also say that displacement is the shortest path that a body can cover between two different points.