TDK - Introduction to Two Dimensional Kinematics

Two Dimensional Kinematics Overview

Introduction

In the one dimensional kinematics unit we mastered the use of the kinematic equations, used them to solve problems of motion in straight horizontal lines and solved "freefall" problem in the vertical direction. In this unit, we will introduce motion in a second dimension to model and predict the more complex motion of projectiles. This will allow the analysis of general motion along a plane, either in the absence of a gravitational field or on the surface of the earth, as well as a very important class of problems called projectile motion.

Essential Questions

1. What is a scalar?
2. What is a vector?
3. What are examples of physical quantities that are represented by vectors and scalars?
4. How are vectors represented?
5. How does one convert from one representation of a vector to another?
6. How are vectors added and subtracted?
7. How many kinematic equations are required for two dimensional motion?
8. Which variables in the kinematic equations require subscripts, that is, which are vectors?
9. Which variables do the kinematic equations have in common for both the x and y directions?
10. What is the acceleration in the y direction for projectile problems?
11. What is the acceleration in the x direction for projectile problems?
12. What launch angle results in the maximum distance for a projectile launched on level ground?
13. What mathematical shape does displacement of a projectile follow?

Key Terms

1. Scalar - A quantity which can be described by a single number.
2. Projectile - An object projected into space by the exertion of a momentary force, subsequently under the influence on only gravity (baseballs, arrows, etc). Complex systems experiencing a continuous force, which will not be considered in this course are also called projectiles (rockets, missiles, etc.).
3. Range - The horizontal distance between the launch point and landing point of a projectile.
4. Relative motion - Motion from the perspective of a given observer.
5. Trajectory - The path a projectile follows through space as a function of time.
6. Vector - Mathematical representation of a physical quantity requiring both magnitude and direction.

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