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Chapter 6 - Chapter 6 Motion in 2 dimensions Position and...

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Chapter 6 - Motion in 2 dimensions. Position and velocity 1 1 1 1 1 2 2 2 2 1 ˆ ˆ ˆ ˆ ; ˆ ˆ ; ˆ ˆ ; x y r r i r j x i y j r x i y j r r r xi y j = + = + = + = - = ∆ + ∆ r r r r r 0 ˆ ˆ ; ˆ ˆ ˆ ˆ lim ; avg x y t r x y v i j t t t r dr dx dy v i j v i v j t dt dt dt = = + = = = + = + r r r r r 2 2 cos ; sin ; ; tan ; x y y x y x dx dy v v v v dt dt v v v v v θ θ θ = = = = = + = s ds V dt = 2 2 ( ) ( ) dx dy V dt dt = +
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Constant acceleration Projectile motion A projectile that is launched with an initial velocity (v ix ,v iy ) follows a parbolic trajectory. v ix =v i cos and v Ѳ iy =v i sin Ѳ The vertical component decreases by 9.8 m/s every second as The gravitational force is 9.8 m/s 2 . The horizontal position is Constant. 0 ; lim ; avg t v v dv a a t t dt = = = r r r r r ˆ ˆ ˆ ˆ ; y x x y dv dv dv a a i a j i j dt dt dt = + = = + r r 1 2 2 ( ) f i ix x fx ix x x x v t a t v v a t = + ∆ + = + 1 2 2 ( ) f i iy y fy iy y y y v t a t v v a t = + ∆ + = + ˆ ˆ ˆ ˆ ˆ ˆ constant i i i i ix iy x y r x i y j v v i v j a a i a j = + = + = + = r r r
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