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Understanding Vector Kinematics: Displacement, Velocity, and Projectile Motion

This chapter explores the fundamentals of vector kinematics, emphasizing quantities such as displacement, velocity, acceleration, force, and momentum, which are defined by both magnitude and direction. Vectors can be visually represented as arrows, with their length indicating magnitude and angle denoting direction. The chapter discusses vector addition techniques, including adding by components and relative velocity concepts. Additionally, it delves into projectile motion, where horizontal and vertical motions are treated separately, highlighting the effects of gravity on projectiles following parabolic paths.

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Understanding Vector Kinematics: Displacement, Velocity, and Projectile Motion

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Presentation Transcript

  1. Chapter 3 2-D Kinematics

  2. Vectors • Quantities described by a magnitude and a direction • Displacement, velocity, acceleration, force, momentum, etc. • Can be represented as an arrow • Length of the arrow = magnitude • Angle of the arrow = direction

  3. Vector Addition • You cannot just add or subtract magnitudes, unless they are directly aligned or directly opposed • To add, draw them tip to tail • The total, “resultant,” vector is drawn from the very beginning to the very end

  4. Vector components • Each vector can be treated as the hypotenuse of a right triangle • Every vector is the resultant of a horizontal and vertical component vector

  5. Adding by components • Find components of all vectors • Rx = Ax + Bx + . . . • Ry = Ay + By + . . . • R2 = Rx2 + Ry2 • tan = Ry/Rx

  6. Relative Velocity • All vectors are measured in reference to a particular place, called a ‘reference frame’

  7. Relative Velocity

  8. Projectile Motion • Falling through the air while moving horizontally • Constant velocity horizontally • Constant acceleration (-9.8 m/s2) vertically • Only consider moment just after launch to the moment just after landing • Projectiles follow parabolic paths

  9. Projectile Motion

  10. Projectile Motion

  11. Projectile Motion • X and Y motions are completely separate • Time is a scalar, so it’s the same for both • Do kinematics separately for each x = vix = vfx = ax = 0 t = y = viy = vfy = ay = -9.8 m/s2 t =

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