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L0parbl - Chapter 4 Kinematics in 2 3 Dimensions Kinematics...

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Chapter 4 Projectile Motion Circular Motion

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Position and Displacement in 3-D
Average Velocity Displacement per unit time Instantaneous velocity v avg = r t = x t ˆ i + y t ˆ j + z t ˆ k v ( t ) = d r dt = dx dt ˆ i + dy dt ˆ j + dz dt ˆ k

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Kinematic equations must be written in vector form Unit vector form is most advantageous Takes advantage of properties of Cartesian coordinates; i.e., independence of coordinates from one another r t ( 29 = x t ( 29 ˆ i + y t ( 29 ˆ j v t ( 29 = d r t ( 29 dt = dx t ( 29 dt ˆ i + dy t ( 29 dt ˆ j = v x t ( 29 ˆ i + v y t ( 29 ˆ j a t ( 29 = d v t ( 29 dt = dv x t ( 29 dt ˆ i + dv y t ( 29 dt ˆ j = a x t ( 29 ˆ i + a y t ( 29 ˆ j
In projectile motion the x and y components of motion are independent Use vector notation for position and velocity 0 0 0 0 cos sin x y v v v v θ = = v 0 = v 0 x ˆ i + v 0 y ˆ j v t ( 29 = v x t ( 29 ˆ i + v y t ( 29 ˆ j

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L0parbl - Chapter 4 Kinematics in 2 3 Dimensions Kinematics...

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