Question

An ant travels along a right angled triangle $△$ PQR first from P to R, then from R to Q. Find the displacement and distance travelled by the ant?
Given, PR = $13m$, RQ = $12m$

• A. Displacement = $25m$
  Distance = $25m$
• B. Displacement = $25m$
  Distance = $5m$
• C. Displacement = $5m$
  Distance = $25m$
• D. Displacement = $5m$
  Distance =$5m$

Answer 1

The correct option is C Displacement = $5m$

Distance = $25m$
Given, the distance PR = $13m$, and RQ = $12m$
$\therefore$ the total distance travelled = PR + RQ = $13+12$ = $25m$.

The initial position is P, and the final position is Q.
The shortest distance between the initial and the final positions is the displacement.
$\therefore$ the total displacement = PQ = $\sqrt{{13}^2-{12}^2}$ = $\sqrt{25}$ = $5m$ (using Pythagoras theorem)
$\therefore$ the distance covered by the ant is $25m$, and the displacement is $5m$.