Physics
Physics
Problem
In a public garden the tile lines form two sets of straight paths that cross each other at right angles. One set of paths runs 45° north of east, and the other set runs 45° north of west. A boy starts from a drinking fountain located at the intersection of two such paths. He walks 4 m along a path that runs 45° north of east, then makes a 90° left turn and walks 3 m along the next path. Using this information, answer the following: a. (i) Find the total distance covered by the boy. b. (ii) Calculate the magnitude of his resultant displacement from the drinking fountain. c. (iii) Compare the values obtained in (i) and (ii) and state which one is larger.Intuitive explanation
The key is to set up a coordinate system aligned with the actual tile paths, not the compass directions. Since the two path sets are perpendicular to each other and tilted 45° from the cardinal directions, you can use them as your and axes—this transforms a tricky geometry problem into simple addition. Once you track the boy's displacement along each path direction, converting back to standard coordinates (or just using path distances) gives you his final position relative to the fountain.
Intuitive explanation
The key is to set up a coordinate system aligned with the actual tile paths, not the compass directions. Since the two path sets are perpendicular to each other and tilted 45° from the cardinal directions, you can use them as your and axes—this transforms a tricky geometry problem into simple addition. Once you track the boy's displacement along each path direction, converting back to standard coordinates (or just using path distances) gives you his final position relative to the fountain.