Question

3. On a square track of edge length 100 m, an athlete
starts from one corner and reaches diagonally
opposite corner. Find the distance and the
magnitude of displacement of the athlete.​

Answer 1

Let PQRS be the square track.

• PQ = QR = RS = SP ⇒ 100 m

$\large{\underline{\textsf{\textbf{ Given \: Information }}}}$

• Edge of the square track = 100 m.

• An athlete starts from one corner and reaches diagonally opposite corner.

$\large{\underline{\textsf{\textbf{ To \: Calculate }}}}$

• Distance travelled

• Displacement

$\large{\underline{\textsf{\textbf{ Calculation : }}}}$

According to the question,

» An athlete starts from one corner and reaches diagonally opposite corner.

Suppose that he starts from point P. So, the corner diagonally opposite to point P is point R. Therefore,

$\longrightarrow \sf { Distance \: Travelled = PS + SR }$

$\longrightarrow \sf { Distance \: Travelled = (100 + 100) \: m }$

$\longrightarrow \sf \red { Distance \: Travelled = 200 \: m }$

Now, finding the his displacement.

As we know that,

» Displacement is the shortest path between the body's intial position and the final position.

PR is the shortest path between the athlete's final and the inital position.

By pythagoras property, we can find the length of PR.

$\longrightarrow \sf { Displacement = \sqrt{PS^2 + SR^2 }}$

$\longrightarrow \sf { Displacement = \sqrt{(100)^2 + (100)^2 } \: m}$

$\longrightarrow \sf { Displacement = \sqrt{10000+ 10000 } \: m}$

$\longrightarrow \sf { Displacement = \sqrt{20000 } \: m}$

$\longrightarrow \sf { Displacement = \sqrt{2 \times \underline{10 \times 10} \times \underline{ 10 \times 10 }} \: m}$

$\longrightarrow \sf { Displacement = 10 \times 10 \sqrt{2 } \: m}$

$\longrightarrow \sf \red{ Displacement = 100 \sqrt{2 } \: m}$

Therefore,

• Distance ⇒ 200 m
• Displacement ⇒ 100√2 m