need help understanding how to do this problem. "A swimmer swims a half lap, moving from the left end to the right end of a pool that is 50 meters long. What is the distance and what is the displacement? Thanks...
Half a lap is 25 meters. So the distance is 25 m. Where did s/he end up? 25 m from where s/he started. So the displacement is 25 m. I don't know the context of the problem but there could be a + or - sign for the displacement.
A swimmer swims a half lap, moving from the left end to the right end of a pool that is 50 meters long. what is the displacement?
50m is the distance and 50m is the displacement
To find the distance the swimmer traveled, we simply need to determine the length of the path covered. In this case, the swimmer traveled a half lap from the left end to the right end of a 50-meter long pool.
The distance covered is equal to the length of the path taken, which is half of the pool's circumference. The circumference of a circular lap can be found using the formula C = πd, where C is the circumference and d is the diameter. Since we're given the length of the pool (50 meters), we can determine the diameter of the pool using the formula d = 2r (where r is the radius, half the diameter).
The diameter of the pool is twice the length of the pool, so d = 2 * 50 = 100 meters. Hence, the circumference is C = π * 100 = 314.16 meters. Since the swimmer covered half of this circumference, the distance traveled is 314.16 / 2 = 157.08 meters.
Now, to understand the displacement, we need to consider the final and initial positions of the swimmer. The swimmer started at the left end of the pool and ended at the right end. Displacement refers to the straight-line distance from the initial to the final position (regardless of the path taken).
Since the swimmer traveled horizontally from left to right, the displacement is simply the length of the pool from left to right, which is 50 meters.
To summarize:
- The distance traveled by the swimmer is 157.08 meters.
- The displacement of the swimmer is 50 meters.