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Welcome back to Physics 211

Welcome back to Physics 211. Today’s agenda: Announcements Velocity and acceleration in two-dimensional motion Motion under gravity. Describing motion with vectors. Positions and displacements D s = s F - s I Velocities and changes in velocity:

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Welcome back to Physics 211

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  1. Welcome back to Physics 211 Today’s agenda: Announcements Velocity and acceleration in two-dimensional motion Motion under gravity

  2. Describing motion with vectors • Positions and displacements Ds = sF - sI • Velocities and changes in velocity: vav= Ds/Dt vinst= limDt->0Ds/Dt Dv = vF - vI • aav= Dv/Dt ainst= limDt->0Dv/Dt

  3. 2D Motion Note: component of position vector along x direction is the x coordinate! y s – vector position s=xi+yj  v=vxi+vyj x

  4. 2D Motion in components • x and y motions decouple • vx=Dx/Dt; vy=Dy/Dt • ax=Dvx/Dt; ay=Dvy/Dt • If acceleration is only non-zero in 1 direction – can choose coordinates so that 1 component of accel. is zero • Eg . motion under gravity

  5. Simplest case • 2D motion with constant acceleration • Describes motion of ball under gravity (close to surface of Earth) • i.e x and y components of position vector satisfy const accel. equations …

  6. Motion under gravity ax=0 vFx=vIx xF=xI+vIxt ay=-g vFy=vIy-gt yF=yI+vIyt-1/2gt2 y vIy=vsin(q) vIx=vcos(q) v q x

  7. Ball A is released from rest. Another identical ball (ball B) is thrown horizontally at the same time and from the same height. Which ball will reach the ground first? 1. Ball A 2. Ball B 3. Both balls reach the ground at the same time. 4. The answer depends on the initial speed of ball B.

  8. DEMO: Two balls

  9. A ball is thrown vertically upward from a cart at rest. The ball goes up, reaches its highest point and returns to the cart. In a second experiment, the cart is moving at constant velocity and the ball is thrown in the same way, where will the ball land? 1. In front of the cart. 2. Behind the cart. 3. Inside the cart. 4. The outcome depends on the speed of the cart.

  10. DEMO: throwing the ball

  11. Projectile motion R : when is y=0 ? t(vy1-1/2gt)=0 => hmax (y eqn) i.e T=2vsinq/g => R (x eqn.)

  12. Maximum height and range

  13. A battleship simultaneously fires two shells at enemy ships. If the shells follow the parabolic trajectories shown, which ship will be hit first? 1. A 2. Both at the same time 3. B 4. need more information

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