a sensor or an idea for detect how far a human is moved

This is helpful.

You say it is for a school competition.

What level is the school, that is, approaches that might be applicable to a university engineering program might be over reach for a general high school program?

Can you expand on that and/or post the problem statement/rules for the competition?

Is the participant expected to navigate a particular fixed and defined course?

Are there obstacles and will the positions of the obstacles be known or will the system need perform obstacle detection of some sort?

How large will the area for the trials be?

An array of QRcodes or other unique fiducials?

The BBC had a such a system for locating free-moving cameras in "virtual" studios, where the studio camera had another camera that looked vertically up at a system of bullseyes.
Must've been back in the late 1980s, early 90s.
Can't remember the name of the system.

A broad concept would be to have a 3D accelerometer/compass/gyroscope device on each foot and use that to estimate the direction and displacement of each step. The issue with inertial navigation systems like this is that they tend to drift, particularly in velocity, increasingly with time. A foot, nominally stops moving for a moment with each foot plant and that could be used to nominally remove velocity drift.

Even so, this sort of navigation system will degrade in absolute accuracy pretty quickly which is why the time duration of the event and the distance to be traveled are relevant to evaluating whether it might be applicable.

True, except a blind person walking in unknown environment always uses a foot to detect an object that might cause tripping.
My college math/physics lost his sight at age 15 years. He always navigated a classroom that way as a student might have left a chair/stool in his way. At home, he always went by memory, unless someone had moved something.
Paul

8th grade
School does not matter. My goal is to bring rank in the province

yes
yes

this is my friend's task and he did it well

200 to 400 meters

it came to my mind but . it's useless

Odd that a respected broadcasting organisation should adopt a "useless" system.

do you think there is a problem in a slow walk at a distance of 200 meters?

i have nothing to do with that part at the moment . But my friend will probably solve it with an ultrasonic sensor