Final answer:
The runner's displacement after running 1/4 of the way around a circular track with a 50m radius, forming a right triangle inside the track, can be calculated using the Pythagorean theorem and is approximately 70.71m.
Step-by-step explanation:
The displacement of the runner who has run 1/4 of the way around a circular track with a radius of 50m can be found by using the concept of a right-angled triangle. Since the runner covers 1/four of the circumference, this bureaucracy a 90-diploma attitude inside the music that's the nook of the proper triangle. The two sides of the triangle that meet at the right angle are radii of the circle, and hence each will be 50m long. The displacement is the straight line distance from the starting point to the finish point of the run, which is the hypotenuse of the right triangle. To calculate it, you can use the Pythagorean theorem, which states that in a right-angled triangle, the square of the duration of the hypotenuse (c) is same to the sum of the squares of the alternative sides (a and b). Thus, the formula is c = √(a² + b²). Plugging in the values a = 50m and b = 50m, the displacement c would be c = √(50m² + 50m²) = √(2500m² + 2500m²) = √(5000m²) = 70.71m (approx.).