A road is in a Circular form reaching from A to B, with radius of \( 1,4 \mathrm{~km} \) a) Calculate the distance and the displacement from A to B hint: Circumference of Circle \( =2 \pi r \)

Sure, let's solve the problem step by step. ### **Given:** - **Radius of the circular road (r):** 1.4 km - **Circumference of the circle (C):** \( C = 2\pi r \) ### **Assumptions:** Since the problem doesn't specify the exact positions of points A and B on the circular road, we'll assume that they are positioned such that moving from A to B along the road covers half of the circle. This means that the angle subtended at the center by points A and B is 180 degrees (i.e., they are at opposite ends of a diameter). This is a common scenario in such problems unless stated otherwise. ### **a) Calculating Distance and Displacement from A to B** 1. **Distance from A to B:** - **Definition:** Distance along the path of the road from A to B. - Since A and B are assumed to be endpoints of a diameter, traveling from A to B along the road would cover half the circumference of the circle. - **Calculation:** \[ \text{Distance} = \frac{C}{2} = \frac{2\pi r}{2} = \pi r \] \[ \text{Distance} = \pi \times 1.4 \approx 4.398 \text{ km} \] 2. **Displacement from A to B:** - **Definition:** The straight-line distance from point A to point B, which is the shortest path between them. - Since A and B are at opposite ends of the diameter, the displacement is equal to the length of the diameter. - **Calculation:** \[ \text{Diameter} = 2r = 2 \times 1.4 = 2.8 \text{ km} \] \[ \text{Displacement} = 2.8 \text{ km} \] ### **Summary:** - **Distance from A to B:** Approximately **4.398 km** - **Displacement from A to B:** **2.8 km** ### **Final Answer:** a) The distance traveling along the road from A to B is π × 1.4 km ≈ 4.398 km, and the displacement (straight-line distance) from A to B is twice the radius, 2 × 1.4 km = 2.8 km.