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Unformatted text preview: CH4 Review
Motion in Two and Three Dimensions
Prepared By: Fady Morcos Velocity & Acceleration Components • Average Velocity: vx = • Instantaneous Velocity: ∆x ∆t ∆y vy = ∆t vx = dx dt dy vy = dt • Instantaneous speed in 2D:
2 2 v = vx + v y • Similar treatment for acceleration:
ax = ay = dv x dt dv y dt Velocity & Acceleration Vectors • Assume a position of a particle is defined by: ˆ r = xi + y ˆ j
• Then the velocity vector can be represented by: ˆ j v = vx i + vy ˆ
• Similarly, the accel. vector can be represented in components form: ˆ a = ax i +ay ˆ j Motion with Constant Acceleration • Suppose the velocity vector of a particle at some time t is given by: v = v 0 + at where in terms of component, v x = v0 x + a x t v y = v0 y + a y t similarly, position can be represente d by : 1 a xt 2 2 1 y = y 0 + v0 y t + a y t 2 2 which can be regarded as components of the following vector equation : 1 r = r0 + v 0t + at 2 2 x = x0 + v0 x t + Motion of Projectiles vx = v0 x x = x0 + v0 xt v y = v0 y − gt 12 y = y0 + v0 y t − gt 2 Motion of Projectiles t flight = y max x max 2 v 0 sin θ g 2 v 0 sin 2 θ = 2g 2 2 v 0 sin θ cos θ = g • • Maximum range is achieved at an elevation angle θ = ? Elevation angles that are equal amounts from θmax range yield equal ranges. ...
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 Fall '08
 Turner
 Physics, Acceleration

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