an athlete completes one round of circular track of diameter 200m in 40s. what will be the distance covered and the displacement at the end of 2minutes 20s
Answers
An athlete completes one round of a circular track of diameter 200m in 40s.
Given that, the diameter is 200 m. So, the radius is 100 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 × 100
→ 4400/7
→ 628.571 m
Distance covered in 1 second (during first or one round) = 628.571/40 = 15.714 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. 200 m.
Distance covered in 2min 20sec or 140 sec = 15.714 × 140 = 2199.96 = 2200 m (approx.)
Answer:
YOUR QUESTION :
An athlete completes one round of circular track of diameter 200m in 40s. what will be the distance covered and the displacement at the end of 2minutes 20s.
SOLUTION :
Given :-
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 seconds
Number 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.