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Presentation CHAPTER3

# Presentation CHAPTER3 - CHAPTER 3 MOTION IN TWO AND THREE...

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1 CHAPTER 3 MOTION IN TWO AND THREE DIMENSIONS Displacement Velocity Acceleration Projectile Motion Circular Motion

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2 DISPLACEMENT, VELOCITY, AND ACCELERATION The position vector. Displacement vector Average velocity vector Instantaneous velocity vector j y i x r + = 1 2 r r r - = t r v av = dt r d t r v t = = 0 lim ( 29 ( 29 j y i x j y y i x x r r r + = = - + - = - = 1 2 1 2 1 2 j y i x j y i x r r r ˆ ˆ ˆ ˆ 1 1 2 2 1 2 - - + = - =
3 As Δ t approaches to zero angle between tangent of curve in point x,y and Δ r also approaches zero. x y y x y x t t t t v v by define velocity vector of direction v v v j v i v v j dt dy i dt dx v j t y i t x t j y i x t r v 1 2 2 0 0 0 0 tan ˆ ˆ ˆ ˆ ˆ lim ˆ lim lim lim - = + = + = + = + = = + = = θ Instantaneous velocity vector Magnitude of velocity vector θ

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4 Displacement along x and y axis at motion in 2D with constant acceleration define by For displacement vector Finally we can define displacement vector as function of time and acceleration ( 29 ( 29 2 2 2 2 0 0 2 0 2 0 t j a i a t j v i v r j y i x r t a t v y and t a t v x y x y x y y x x + + + = + = + = + = ˆ ˆ ˆ ˆ ˆ ˆ 2 2 0 t a t v r + = 2 2 2 0 0 2 0 0 t a t v r r t a t v r r r + + = + = - =
5 2 2 2 0 0 0 0 0 ˆ ˆ ˆ ˆ ˆ ˆ ˆ lim ˆ lim ˆ lim ˆ lim lim z y x z y x t t t t t v v v v k v j v i v v k dt dz j dt dy i dt dx v k t z j t y i t x t k z j y i x t r v + + = + + = + + = + + = = + + = = Vector velocity in 3D. i ˆ j ˆ k ˆ k z j y i x r ˆ ˆ ˆ + + = The position of object defines with position vector at any instant. Object move from P1 to position P2. 1 2 r r r - = Instantaneous velocity vector Magnitude of velocity vector v z +v x v

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6 The blue curve shows the path of an object in two dimensions. Which of the vector diagrams best represents the displacement vector from positions P 1 to P 2 ? (1) (3) (2) (4) r r 1 - r 2 r 2 r r r r 1 r 1 -r 1 r 2 r 2 1 2 3 4 None of the diagrams represents the change.
7 Relative Velocity Reference frame The velocity of the person relative to the ground is equal to the velocity of the person relative to the car plus the velocity of the car relative the ground. walkway 21 v v v wg pg + =

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8 During a heavy rain, the drops are falling at a constant velocity and at an angle of 10 ° west of the vertical. You are walking in the rain and notice that only the top surfaces of your clothes are getting wet. In what direction are you walking? What is your walking speed if the speed of the drops relative to the ground is 5.2 m/s?
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