L4F11 - P123F11Lecture4 23Sept2011...

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1 P123 F11 Lecture 4 23 Sept 2011 Projectile Motion: Relative Velocity Topics from previous lecture • Vectors: Quantity with magnitude and direction • Vector addition • Components • Unit vectors •2DMo t ion Position vector: Displacement: r 1 2 r r r k A j A i A A k j i z y x ˆ ˆ ˆ ˆ , ˆ , ˆ A C A - C A B A B C B A dt v d a t v a dt r d v t r v av av
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2 0 v 2 v 0 2 v v i CLICKER
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3 Suppose v o is purely in x -direction. What happens?? Projectile motion • Motion of object in presence of gravity with both vertical and horizontal components Intuition: Path of motion ( trajectory ) is an arc ( baseball, fireworks cannon ball, ski jump,… ) Assumptions: (Neglect air resistance) j g j g i a ˆ ˆ ) ( ˆ 0 g a a y x 0 What is the shape of the trajectory? Conclusion:
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5 Projectile motion is superposition of independent x - motion and y - motion ! Where: Let’s do the math … Initial Conditions: Trajectory : y = f ( x ) ; range = R ; height = h Solve x and y independently: g a o a y x ; o o oy o o ox v v v v sin ; cos 2 2 1 2 2 1 ) sin ( sin ) cos ( cos gt t v gt
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L4F11 - P123F11Lecture4 23Sept2011...

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