A body covered a distance of z metre along a semicircular path. Calculate the magnitude of displacement of the body, and the ratio of distance to displacement?

The displacement of a body moving along a semicircular path is the straight line distance from the starting point to the ending point. In this case, it is the diameter of the semicircle.

Step 1: Calculate the circumference of the full circle The circumference of a full circle is given by the formula 2πr, where r is the radius of the circle. Since the body covered a distance of z meters along a semicircular path, the circumference of the full circle is 2z.

Step 2: Calculate the radius of the circle The radius of the circle is given by the formula C/2π, where C is the circumference of the circle. Substituting the value of C from step 1, we get r = 2z/2π = z/π.

Step 3: Calculate the displacement The displacement of the body is the diameter of the circle, which is twice the radius. Therefore, the displacement is 2r = 2z/π.

Step 4: Calculate the ratio of distance to displacement The ratio of distance to displacement is given by z/(2z/π) = π/2.

So, the magnitude of displacement of the body is 2z/π meters, and the ratio of distance to displacement is π/2.