Question

an athlete complete one round of a circular track of diameter 100m in 40 second what will be the diameter covered and the displacement at the end of 2 min 20 sec

Answer 1

Correct Question

An athlete complete one round of a circular track of diameter 100 m in 40 second. What will be the distance covered and the displacement at the end of 2 min 20 sec?

Solution

An athlete completes one round of a circular track of diameter 100m in 40s.

Given that, the diameter is 100 m. So, the radius is 50 m (half of diameter).

As the athlete covers the path in a circular motion. So, the displacement is zero.

Distance cover in one round (during 40 seconds) = 2πr

(2πr = Circumference of the circle)

→ 2 × 22/7 × 50

→ 2200/7

→ 314.28 m

Distance covered in 1 second (during first or one round) = 314.28/40 = 7.86 m

We have to find the distance covered and the displacement at the end of 2min 20s.

Displacement is zero (as the path is circular). But the athele covers 3.5 rounds (140/40). So, the displacement of the athele is equal to it's diameter of circle i.e. 100 m.

Distance covered in 2min 20sec or 140 sec = 7.86 × 140 = 1100.4 m

Answer 2

$\sf\star\bold\red{\underline{{QUESTION:-}}}$

✓✓An athlete complete one round of a circular track of diameter 100m in 40 second what will be the diameter covered and the displacement at the end of 2 min 20 sec.

$\sf\star\bold\blue{\underline{{GIVEN:-}}}$

• $\sf\: Diameter=100m$

• $\sf\therefore\:radius=\dfrac{Diameter}{2}$

• $\sf\:radius=\dfrac{100}{2}$

• $\sf\:radius=50m$

• Time of one rotation=40 sec.

• Time after 2 min 20 sec = 2×60sec + 20 sec= 140 sec.

$\sf\star\bold\green{\underline{{To\:FIND:-}}}$

• Distance after 140 sec = ?

• Displacement after 140 sec = ?

we know that velocity along a circular path

$\sf\:=\dfrac{Circumference}{Time}$

$\sf\implies\:v=\dfrac{2πr}{40\:sec}$

$\sf\implies\:v=\dfrac{2\times\:3.14\times\:50m}{40\:sec}$

$\sf\implies\:v=\dfrac{314\:m}{40\:sec}$

$\sf\implies\:v=7.85\:m/s$

Distance after 140s,

$\sf\:we\:know\:that\:distance\:=\:velocity\times\:time$

$\sf\implies\: Distance=7.85m/s\times\:140\:sec$

$\sf\implies\: Distance=1099m$

Displacement after 2 m 20 s i.e. in 140 s,

Since,rotation in 40 s = 1

Therefore, rotation in 1 sec =$\sf\dfrac{1}{40}$

$\sf\therefore\: rotation\:in\:140\:sec=\dfrac{1}{40}\times\:140$

$\sf\=3.5$

Therefore, in 3.5 rotations athlete will be just at the opposite side of the circular track, i.e. at a distance equal to the diameter of the circular track which is equal to 100 m.

Therefore, Distance covered in 2 m 20 s = 1099 m.

And, displacement after 2 m 20 s = 100 m