what is the magnitude of displacement and the distance travelled of a body which travels 8m from A toB then moves a distance of 6m at right angles to AB.
That would be the hypotenuse (c) of a right triangle with short sides a = 8 and b = 6.
c^2 = a^2 + b^2 = 64 + 36 = 100.
c = ___
To find the magnitude of displacement and the distance traveled, let's break down the motion into two components:
1) The motion from A to B, which covers a distance of 8m.
2) The motion from B, perpendicular to AB, which covers a distance of 6m.
The magnitude of displacement refers to the shortest distance between the initial and final positions. In this case, the magnitude of displacement is the straight-line distance from A to B.
To calculate the magnitude of displacement:
1) Use the Pythagorean theorem: the square of the magnitude of displacement equals the squares of the two sides of a right-angled triangle.
2) In this case, one side is the distance from A to B (8m), and the other side is the distance from B to C (6m).
3) Therefore, the magnitude of displacement is √(8^2 + 6^2) = √(64 + 36) = √100 = 10m.
The distance traveled is the total path length covered during the entire motion. In this case, we need to sum up the distance from A to B (8m) and the distance from B to C (6m).
Therefore, the distance traveled is 8m + 6m = 14m.
So, the magnitude of displacement is 10m, while the distance traveled is 14m.