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Two Dimensional Dynamics

Two Dimensional Dynamics. y. x. 2-Dimensions. X and Y are INDEPENDENT! Break 2-D problem into two 1-D problems. 7. Kinematics in Two Dimensions. x = x 0 + v 0x t + 1/2 a x t 2 v x = v 0x + a x t v x 2 = v 0x 2 + 2a x  x. y = y 0 + v 0y t + 1/2 a y t 2

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Two Dimensional Dynamics

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  1. Two Dimensional Dynamics

  2. y x 2-Dimensions • X and Y are INDEPENDENT! • Break 2-D problem into two 1-D problems 7

  3. Kinematics in Two Dimensions • x = x0 + v0xt + 1/2 axt2 • vx = v0x +axt • vx2 = v0x2 + 2axx • y = y0 + v0yt + 1/2 ayt2 • vy = v0y +ayt • vy2 = v0y2 + 2ayy x andymotions areindependent! They share a common time t 21

  4. Projectile Motion Demo One marble is given an initial horizontal velocity, the other simply dropped. Which marble hits the ground first? A) dropped B) pushed C) They both hit the ground at the same time When ball hits depends on y only! y(t) = y0 + vyo + ½ ay t Same for both balls! 35

  5. Example: ball thrown from cliff • Use y components to find time vo= 20 m/s • Use x velocity and time to find horizontal distance 60m

  6. Vo=30m/s 200 Example: projectile Vo=30m/s Δy 200 Δx • Break Vo into x & y components

  7. Example: projectile Vo=30m/s Δy • 200 Δx

  8. Vo=50m/s 400 Example: golf shot • Will the ball get over the tree? 20m Vo=50m/s 400 30m

  9. Example: golf shot • Will the ball get over the tree? 20m Vo=50m/s 400 30m

  10. Summary of Concepts • X and Y directions are Independent! • Position, velocity and acceleration are vectors • “Share” t • F = m a applies in both x and y direction • Projective Motion • ax = 0 in horizontal direction • ay = g in vertical direction 50

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