Question bank: Movement of Objects and People

During the Physical Education class, the students of a 2nd grade elementary school class participated in a relay race in the schoolyard. The schoolyard is rectangular and measures 40 meters in length and 20 meters in width. Each student needed to run from the start to the end of the schoolyard and, upon reaching there, touch the hand of the next classmate who was standing at the end. If the class had 8 students, and the last student in line needed to run back to the start so the first student could begin their race, how many meters would the last student have run in total considering only the way to the end of the schoolyard and the way back to the start, without considering the return to the end of the schoolyard? Consider that all students run at a constant speed and that the last student starts their race immediately after the touch.

In the city of Mathematics, there is a square with four sculptures at different points, A, B, C, and D, which are used as reference points to indicate directions. João walks 20 steps north from point A to point E. Then, he walks 15 steps east to point F. Next, he decides to return to point A, but instead of following the way back, he walks 30 steps west and 5 steps south, ending up at a point we will call G. Considering that each of João's steps is the same size and he does not take steps diagonally, what is the total distance, in steps, that João travels from point E to point G, passing through point F? Consider that he travels the shortest distance possible between two points.

João is at the playground and wants to reach the newspaper stand, which is 10 steps away. He takes 3 steps forward, then 2 steps back, and finally takes 5 more steps forward. Based on this, describe how João moved around the playground and explain the reference points he used to decide the steps he took.

João is playing in the park and decides to walk in a straight line from the bench where he is sitting to the slide. After the displacement, he realizes that the bench is now exactly behind him, in the same direction and sense that he was initially sitting. Considering that the bench did not move and that João moved in a straight line, how can we describe João's movement from the bench to the slide and what is the spatial relationship between the slide, the bench, and the point where João was initially sitting?

In school, teacher Ana placed some toys in a box to take to the next room. She walked straight to the next room, turned left, walked a little further, and finally stopped to open the box. Describe the path that teacher Ana took, imagining you are a bird flying above. Remember to include reference points, such as the direction she was facing and the direction she moved in.