2D Particle Kinematics Projectile Motion

# 2D Particle Kinematics Projectile Motion - 2D Particle...

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2D Particle Kinematics – Motion in x-y coordinates Position: coordinates of the particle ( x ( t ), y ( t ) ) Vector definition – position vector 22 ˆˆ () () , tan / rt xti yt j r x y y x θ = += + = Velocity: average velocity 21 ave rr r ttt υ = = ∆−  , instantaneous velocity , tan / xy x y x y yx dr ij dt dx dy dt dt υυ υ υ υ αυυ = = + ⇒= = = + = Acceleration: average acceleration ave a t tt = = , instantaneous acceleration 2 2 tan / y x x y x y d a ai a j dt dt d d dx dy a a a a a aa dt dt dt dt β = = = + = = = = + Projectile motion Horizontal motion – constant velocity: 00 0 0 cos ( cos ) x x a xx t υυ α υα = = = + Vertical motion – constant acceleration: 2 0 0 sin 1 ( sin ) 2 ( sin ) 2 ( ) y y y ag gt y y t gt gy y υυα = − = = +− = NOTE: 1. Projectile motion is determined by its initial velocity: υ 0 and α 0 . 2. The initial angle α 0 is positive/negative if the projectile is launched above/below the horizontal.

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2D Particle Kinematics Projectile Motion - 2D Particle...

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