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🔋college physics i – introduction review

Resultant Displacement

Written by the Fiveable Content Team • Last updated September 2025
Written by the Fiveable Content Team • Last updated September 2025

Definition

Resultant displacement is the net or combined displacement experienced by an object that is undergoing motion in two or more dimensions. It represents the overall change in position of the object from its initial location to its final location, taking into account the individual displacements along each axis.

5 Must Know Facts For Your Next Test

  1. Resultant displacement is calculated by using vector addition to combine the individual displacements along the x and y axes.
  2. The magnitude of the resultant displacement is determined by the Pythagorean theorem, using the x and y displacements as the sides of a right triangle.
  3. The direction of the resultant displacement is given by the angle between the resultant vector and the positive x-axis, which can be calculated using trigonometry.
  4. Resultant displacement is an important concept in kinematics, as it allows for the analysis of motion in two dimensions, such as projectile motion and circular motion.
  5. Understanding resultant displacement is crucial for solving problems involving the net change in position of an object, which is often required in introductory physics courses.

Review Questions

  • Explain how to calculate the magnitude of the resultant displacement of an object moving in two dimensions.
    • To calculate the magnitude of the resultant displacement, you need to first determine the individual displacements along the x and y axes. Then, you can use the Pythagorean theorem to find the length of the resultant displacement vector. Specifically, the magnitude of the resultant displacement is given by the formula: $\sqrt{\Delta x^2 + \Delta y^2}$, where $\Delta x$ and $\Delta y$ are the displacements along the x and y axes, respectively.
  • Describe the relationship between the individual displacements and the direction of the resultant displacement.
    • The direction of the resultant displacement is determined by the relative magnitudes and directions of the individual displacements along the x and y axes. Specifically, the angle between the resultant displacement vector and the positive x-axis can be calculated using trigonometry, such as the inverse tangent function: $\theta = \tan^{-1}(\Delta y/\Delta x)$, where $\theta$ is the angle of the resultant displacement and $\Delta x$ and $\Delta y$ are the individual displacements. The direction of the resultant displacement is then given by this angle, which can be used to determine the overall change in position of the object.
  • Analyze how the concept of resultant displacement is applied in the context of projectile motion.
    • In the study of projectile motion, the concept of resultant displacement is crucial for understanding the trajectory of an object, such as a ball or a projectile. The horizontal and vertical displacements of the projectile can be treated as individual displacement vectors, which can then be combined using vector addition to determine the resultant displacement. This allows for the prediction of the object's landing position, range, and other important characteristics of its motion. Understanding resultant displacement is therefore essential for analyzing and solving problems involving projectile motion, which is a common topic in introductory physics courses.