Find distance and length of straightaway

Question

There is a 1000.00- meter track. The track consists of two semicircles and two equal and parallel straightaways, AB and CD.

 

A. - Find the length of each straightaway 

 

B. - Find the distance L

 

(L is the entire track from end to end)

 

(The middle height of the track is 50.00 M)

 

 

Answer 1

The 1000-meter length of the track is composed of three parts: the first semicircle, the parallel straightaways, and the second semicircle. Those two semicircles together make up a single circle, so we can express the length of the track as:

 

1000 = (circumference of circle) + 2(length of one straightaway)

 

 

Let's call the length of one straightaway x. The middle height of the track, 50 meters, is the circle's radius. So:

 

1000 = 2πr + 2x

1000 = 2π(50) + 2x

1000 = 100π + 2x

1000 - 100π = 2x

500 - 50π = x

 

The length of one straightaway is x = 500 - 50π ≈ 342.92 meters.

 

 

The length of the track from end-to-end is the length of one straightaway plus two radii (one for each semicircle):

 

L = x + 2r

L = 342.92 + 2(50)

L = 442.92

 

The track's length is approximately 442.92 meters.