Question

uispluccci
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.
4. In the above question if the athlete reaches back to
the same corner after running on the track once,
find the distance and magnitude of displacement of
the athlete.​

Answer 1

Required Solution :

⑶

Given that an athlete starts from one corner and reaches diagonally opposite corner on a square track. The measure of the sides of the square is 100 m each.

[Figure 1] Let's assume that he starts from Corner A. The corner diagonally opposite to Corner A is Corner C. So, he ran from A to C.

Total Distance :

We know that,

• Distance is the total length of path covered by a body irrespective of the direction in which it travels.

So, as he travelled from A to C then,

$\dashrightarrow$ Total Distance = AB + BC

$\dashrightarrow$ Total Distance = 100 m + 100 m

$\dashrightarrow \boxed{\sf { Total \: Distance = 200 \: m} }$

Therefore, total distance covered by the body is 200 m.

Displacement :

According to the question, his initial position is corner A and his final position is corner C.

• Displacement is the shortest distance between its initial and its final position. We can also say that, the shortest distance between its initial and its final position is straight line path.

[Figure 1] Shortest distance between corner A and corner C is a straight line path, that is the diagonal of the square track (AC).

$\dashrightarrow \sf { (AC)^2 = (AB)^2 + (BC)^2 }$

$\dashrightarrow \sf { (AC)^2 = (100)^2 + (100)^2 }$

$\dashrightarrow \sf { (AC)^2 = 10000 + 10000 }$

$\dashrightarrow \sf { (AC)^2 = 20000 }$

$\dashrightarrow \sf { AC = \sqrt{20000} }$

$\dashrightarrow \sf { AC = \sqrt{2 \times 10 \times 10 \times 10 \times 10} }$

$\dashrightarrow \sf { AC = 10 \times 10\sqrt{2} }$

$\dashrightarrow \sf { AC = 100\sqrt{2} }$

$\dashrightarrow \boxed{\sf { Displacement = 100 \sqrt{2} \: m} }$

⑷

According to the question, the athlete back to the same corner after running on the track once. We have to find distance travelled and magnitude of the displacement.

• Distance is the total length of path covered by a body irrespective of the direction in which it travels.

He covers one round as he came back to the same corner after running on the track once. Total length of the track is the total distance travelled in this case. As all the sides of square are equal, so we'll use here the perimeter of the square to find the total length of the track.

$\dashrightarrow \sf { Distance = 4(100) \: m}$

$\dashrightarrow \boxed{\sf { Distance = 400 \: m}}$

Now, we'll be finding magnitude of displacement.

The athlete came back to its initial position(A) after covering a certain distance. So, his displacement is 0 as the shortest distance between his initial (A) and his final position (A) is 0.

$\dashrightarrow \boxed{\sf { Displacement = 0 \: m}}$