The drawing shows a triple jump on a checkerboard, starting at the center of square A and ending on the center of square B. Each side of a square measures 4.8 cm. What is the magnitude of the displacement of the colored checker during the triple jump (there is only one right corner)?
The Correct Answer and Explanation is :
o determine the magnitude of the displacement of the colored checker during the triple jump on a checkerboard, we need to analyze the movement from the center of square A to the center of square B.ach side of a square measures 4.8 cm.he problem specifies that there is only one right corner in the path. Understanding the Path:
triple jump typically consists of three segments: two in one direction and a third that involves a turn, forming a right angle.iven that there’s only one right corner, we can infer that the checker moves two squares in one direction (say horizontally) and then one square perpendicular to that direction (vertically). Calculating the Displacement:
- Horizontal Movement:
- he checker moves two squares horizontally. – ach square side is 4.8 cm, so moving two squares covers a horizontal distance of: [ \text{Horizontal Distance} = 2 \times 4.8, \text{cm} = 9.6, \text{cm} ]
- Vertical Movement:
- he checker then moves one square vertically. – his vertical movement covers a distance of: [ \text{Vertical Distance} = 1 \times 4.8, \text{cm} = 4.8, \text{cm} ]
- Resultant Displacement:
- he horizontal and vertical movements form a right-angled triangle, with the displacement being the hypotenuse. – sing the Pythagorean theorem: [ \text{Displacement} = \sqrt{(9.6, \text{cm})^2 + (4.8, \text{cm})^2} ] [ = \sqrt{92.16, \text{cm}^2 + 23.04, \text{cm}^2} ] [ = \sqrt{115.2, \text{cm}^2} ] [ \approx 10.73, \text{cm} ] Conclusion:
he magnitude of the displacement of the colored checker during the triple jump is approximately 10.73 cm.his displacement represents the straight-line distance from the starting point at the center of square A to the ending point at the center of square B, considering the specified path with one right corner. nderstanding displacement in this context involves recognizing that it is the shortest distance between the initial and final positions, regardless of the actual path taken.n this scenario, even though the checker moves along two sides of the checkerboard squares, the displacement is the direct line connecting the start and end points.his concept is fundamental in physics, distinguishing between the path length (total distance traveled) and displacement (straight-line distance between two points).