5. An athlete runs from one end to the other end of a semicircular track whose radius is 70 m. What is the distance covered by the athlete and what is his displacement?
Answers
Explanation:
Since the athlete is following a semi-circular path, the distance traveled shall be the perimeter of the semicircle:1/2 (2π r)=πr=3.14x70=219.8 m
where r is the radius of the semicircle along which the athlete running.
Displacement: Since the athlete is starting from one end of the semicircle and reaching the other end, his position is displaced by the radius of the semicircle, what is 70m.
• Distance travelled:219.8m
• Displacement=radius of the semicircle=70m
GiveN InformatioN : An athlete runs from one end to the other end of a semicircular track whose radius is 70 m.
To FinD : Distance covered and the displacement.
Suppose that the body starts from point A, so after running from one end to the other end of a semicircular track, it'll come to point B. Thus, we need to find the total length of the semicircular track which will be the total distance covered.
➝ Distance covered = Perimeter of the semicircular track
➝ Distance covered = 2πr ÷ 2
➝ Distance covered = (2 × 22/7 × 70) m ÷ 2
➝ Distance covered = (2 × 22 × 10) m ÷ 2
➝ Distance covered = 440 m ÷ 2
➝ Distance covered = 220 m
Now, we've to calculate displacement. Displacement is the shortest distance from initial position to the final position of the body. Here, initial position is A and final position is B. The shortest distance from A to B will be AB which chan be considered as the diameter of the semicircular track.
➝ Displacement = Diameter
➝ Displacement = 2 × Radius
➝ Displacement = 2 × 70 m
➝ Displacement = 140 m
Therefore,
- Distance covered by the body is 220 m.
- Magnitude of the displacement of the body is 140 m.
