Question

An athlete completes one round of a circular track of diameter 200 m in 40 s. What will be the distance covered and the displacement at the end of 2 minutes 20 s?

P.S- @blueskybutterfly thanks a lot for thanking all my answers. Love ya, sissy!!! :)

Answer 1

Given : -

Diameter of circular path = 200m

Time taken by athlete to complete a revolution = 40s

To Find : -

Distance and displacement of athlete after 2min and 20s.

Solution : -

We know that, Radius = Diameter/2

∴ Radius = 200/2 = 100m

Total time = 2min 20s = 140s

No. of revolutions = 140/40 = 3.5

After 2min 20s, athlete will complete 3.5 revolutions.

Distance travelled : -

$\longrightarrow \sf d = 3.5 \times 2 \pi R \\\\ \longrightarrow d = .5 \times 2 \times 3.14 \times 100 \\\\\longrightarrow d = 3.5 \times 628 \\\\ \longrightarrow d = 2198 m$

Displacement : -

After 3.5 revolutions, athlete will be at the diametrically opposite to the initial position.

$\longrightarrow \sf d^{'} = 2R\\\\ \longrightarrow d^{'} = 2\times 100 \\\\ \longrightarrow d^{'} = 200m$

Answer 2

Explanation:

Diameter of circular track = 200 m

Radius, r = 200/2 = 100 m

Time taken by athlete to complete one round = 40 seconds.

To Find :-

Distance covered = ??

Displacement = ??

Formula to be used :-

Speed = Distance/Time

Circumference of circle = 2πr

Solution :-

2 min 20 seconds = 140 secondsNumber of rounds = 140/4 = 35

⇒ Distance covered = 35 × circumference

⇒ Distance covered = 35 × 2 × 22/7 × 100

⇒ Distance covered = 5 × 2 × 22 × 100

⇒ Distance covered = 22000 m

Hence, the distance covered at the end of 2 min 20 seconds is 22000 m or 22 km.

And displacement is 200 m as it return to initial position again.