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

Sure, here is the step by step solution:

Step 1: Understand the problem The body is moving along a semicircular path. The displacement of the body would be the straight line distance from the starting point to the ending point. In a semicircle, this is the diameter.

Step 2: Calculate the displacement The diameter of a circle (and thus the displacement of the body) is twice the radius. The circumference of a circle is 2πr, and the length of a semicircle is πr. If the body covered a distance of z meters along the semicircle, then z = πr. Solving for r, we get r = z/π. Therefore, the displacement (diameter) is 2r = 2z/π.

Step 3: Calculate the ratio of distance to displacement The ratio of distance to displacement is 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.