‘R walks 1 km. to east and then he turns to south and walks 5 km. Again he turns to east and walks 2 km. After this he turns to north and walks 9 km. How far is he from his starting point ?

To find the distance from the starting point, we calculate the net displacement in the east-west and north-south directions. R first walks 1 km east, then 2 km east, resulting in a total eastward displacement of 3 km [t2]. In the north-south direction, R walks 5 km south and then 9 km north. The net northward displacement is 9 km - 5 km = 4 km [t1]. These two perpendicular components (3 km east and 4 km north) form the legs of a right-angled triangle. Using the Pythagorean theorem (a² + b² = c²), the distance from the starting point is the hypotenuse: √(3² + 4²) = √(9 + 16) = √25 = 5 km [t3]. Thus, R is 5 km away from his starting point. This method of vector addition is standard for determining resultant displacement [t3][t5].