A running track consists of two straight 88.5m segments and two semicircles of radius 39.0m

The distance a runner travels in one complete lap I calculated to be 422 m.

How do you find the displacement in x.y of a runner who covers half a lap?

To find the displacement in x.y of a runner who covers half a lap, you can break down the lap into its individual segments and calculate the distances covered in each segment.

First, let's calculate the distance covered in the straight segments. Since there are two straight 88.5m segments in one full lap, the total distance covered in the straight segments is 2 * 88.5m = 177m.

Next, let's calculate the distance covered in the semicircles. Since the radius of each semicircle is 39.0m, the circumference of each semicircle is 2 * π * 39.0m = 78.0πm. Since there are two semicircles in one full lap, the total distance covered in the semicircles is 2 * 78.0πm.

To find the distance covered in half a lap, we need to divide the total distances by 2:

Distance covered in straight segments = 177m / 2 = 88.5m
Distance covered in semicircles = (2 * 78.0πm) / 2 = 78.0πm

Now, let's calculate the total distance covered in half a lap:

Total distance covered in half a lap = Distance covered in straight segments + Distance covered in semicircles
= 88.5m + 78.0πm

Since π is an irrational number, we cannot calculate the exact value of the displacement in x.y without knowing the value of π. However, we can approximate it using π ≈ 3.14.

Total distance covered in half a lap ≈ 88.5m + 78.0 * 3.14m
≈ 88.5m + 245.52m
≈ 334.02m

Therefore, the approximate displacement in x.y of a runner who covers half a lap is 334.02 meters.

To find the displacement in the x or y direction for a runner who covers half a lap, we need to consider the geometry of the track.

Let's assume that the starting point is at the origin (0, 0) and the x-axis is horizontal, while the y-axis is vertical.

Now, let's break down the track into its individual segments:

1) Straight Segment 1: This segment is 88.5m long and runs parallel to the x-axis. So, the displacement in the x-direction for this segment is 88.5m.

2) Semicircle 1: The radius of the semicircle is 39m. Since the runner is covering half a lap, they will only run through half of the semicircle. The circumference of a semicircle is πr, where r is the radius. Therefore, the circumference of this semicircle is π * 39m = 122.52m. So, the displacement in the x-direction for this semicircle is 122.52m.

3) Straight Segment 2: Similar to Straight Segment 1, the displacement in the x-direction for this segment is also 88.5m.

4) Semicircle 2: This is the second semicircle, and its displacement in the x-direction is the same as that of Semicircle 1, which is 122.52m.

Now, let's calculate the total x-displacement:

Total x-displacement = Straight Segment 1 + Semicircle 1 + Straight Segment 2 + Semicircle 2
= 88.5m + 122.52m + 88.5m + 122.52m
= 422.04m

Therefore, the x-displacement for a runner who covers half a lap is 422.04m.