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🔋college physics i – introduction review

Displacement Angle

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

Definition

The displacement angle is the angle between the initial position vector and the final position vector of an object moving in two-dimensional space. It represents the direction of the object's displacement from its starting point to its ending point.

5 Must Know Facts For Your Next Test

  1. The displacement angle is an important parameter in the analysis of two-dimensional kinematics, as it determines the direction of the object's motion.
  2. The displacement angle is measured counterclockwise from the positive x-axis of the coordinate system.
  3. The displacement angle, along with the magnitude of the displacement vector, can be used to calculate the object's final position coordinates.
  4. In projectile motion, the displacement angle is the angle at which the object is launched relative to the horizontal.
  5. The displacement angle is a key factor in determining the range, maximum height, and other characteristics of a projectile's trajectory.

Review Questions

  • Explain how the displacement angle is defined and how it is measured in a two-dimensional coordinate system.
    • The displacement angle is the angle between the initial position vector and the final position vector of an object moving in two-dimensional space. It is measured counterclockwise from the positive x-axis of the coordinate system. The displacement angle represents the direction of the object's displacement from its starting point to its ending point and is a crucial parameter in the analysis of two-dimensional kinematics.
  • Describe the relationship between the displacement angle and the characteristics of a projectile's trajectory.
    • In the context of projectile motion, the displacement angle is the angle at which the object is launched relative to the horizontal. The displacement angle, along with the initial velocity and the acceleration due to gravity, determines the range, maximum height, and other characteristics of the projectile's trajectory. A higher displacement angle will result in a higher maximum height but a shorter range, while a lower displacement angle will produce a longer range but a lower maximum height.
  • Analyze how the displacement angle can be used to calculate the final position coordinates of an object moving in two-dimensional space.
    • The displacement angle, along with the magnitude of the displacement vector, can be used to calculate the object's final position coordinates. Specifically, the x-coordinate of the final position can be determined by multiplying the magnitude of the displacement vector by the cosine of the displacement angle, while the y-coordinate can be determined by multiplying the magnitude of the displacement vector by the sine of the displacement angle. This allows for the complete reconstruction of the object's path from its initial position to its final position using the displacement angle and the displacement vector.