An athletics track has two straight lengths of 100 m and two semi-circular ends of radius 31.8 as shown below. How many laps will an athlete need to complete in order to finish a 10000 m race? Give your answer correct to the nearest lap
To find out how many laps an athlete will need to complete a 10000 m race on this athletics track, we need to calculate the total distance covered in one complete lap and then divide that into the total race distance.
Let's break it down step by step:
1. Calculate the distance covered in one straight length:
- Each straight length is 100 m.
- The track has two straight lengths, so the total distance covered in the straight lengths is 2 * 100 m = 200 m.
2. Calculate the distance covered in one semi-circular end:
- The radius of each semi-circular end is 31.8 m.
- The circumference of a circle is given by the formula: circumference = 2 * π * radius.
- So, the distance covered in one semi-circular end is 2 * π * 31.8 m = 63.6π m.
3. Calculate the total distance covered in one lap:
- To find the total distance covered in one lap, we need to add the distance covered in the straight lengths to the distance covered in the semi-circular ends.
- Total distance covered in one lap = distance covered in straight lengths + distance covered in semi-circular ends
- Total distance covered in one lap = 200 m + 63.6π m.
4. Calculate the number of laps needed to complete the 10000 m race:
- Number of laps = total race distance / total distance covered in one lap
- Number of laps = 10000 m / (200 m + 63.6π m).
Approximating π to 3.14, we can now calculate the number of laps:
Number of laps = 10000 m / (200 m + 63.6 * 3.14)
= 10000 / (200 + 200.504)
= 10000 / 400.504
≈ 24.97.
Therefore, an athlete will need to complete approximately 25 laps to finish a 10000 m race on this athletics track (rounded to the nearest lap).
2 pi * 31.8 + 200 = 400 meters/lap
10,000 / 400 = 25 laps