How to find resultant displacement |r|?

The concept of displacement can be tricky for many students to understand when they first encounter it in a physics course. This is because in physics, displacement is different from the concept of distance, which many students may have previous experience with. Displacement is a vector quantity, and as such has both a magnitude and a direction. Displacement is defined as the vector (or straight line) distance between an initial and final position. The resultant displacement therefore depends only on knowledge of these two positions.

Determine the position of two points in a given coordinate system. For example, assume an object is moving in a Cartesian coordinate system, and the initial and final positions of the object are given by the coordinates (2,5) and (7,20).

Use the Pythagorean theorem to set up the problem of finding the distance between the two points. The Pythagorean theorem can be written as c^2 = x^2 + y^2, where c is the distance to be found, and x and y is the distance between the two points in the x- and y-axes, respectively. In this example, the value of x is found by subtracting 2 from 7, which gives 5; the value of y is found by subtracting 20 by 5, which gives 15.

Substitute numbers into the Pythagorean equation and solve. In the example above, substituting numbers into the equation gives **c = / 5^2 + 15^2 ,** where the symbol / denotes the square root, and the symbol ^ denotes an exponent. Solving the above problem gives c = 15.8. This is the distance between the two objects.

To find the direction of the displacement vector, calculate the inverse tangent of the ratio of the displacement components in the y- and x-directions. In this example, the ratio of the displacement components is 15/5 and calculating the inverse tangent of this number gives 71.6 degrees. Therefore, the resultant displacement is 15.8 units, with a direction of 71.6 degrees from the original position.