# How to Find Resultant Displacement in Physics

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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.

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