CH4 - Chapter 4 Motion in Two Dimensions Motion in Two...

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Chapter 4 Motion in Two Dimensions
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Chapter 4 Motion in Two Dimensions Suppose the zookeeper must shoot the banana from the banana cannon to the monkey who hangs from the limb of a tree. This particular monkey has a habit of dropping from the tree the moment that the banana leaves the muzzle of the cannon. The zookeeper is faced with the dilemma of where to aim the banana cannon in order to hit the monkey. If the monkey lets go of the tree the moment that the banana is fired , then where should she aim the banana cannon?
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Motion in Two Dimensions Using + or – signs is not always sufficient to fully describe motion in more than one dimension Vectors can be used to more fully describe motion Still interested in displacement, velocity, and acceleration Will serve as the basis of multiple types of motion in future chapters
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Position and Displacement The position of an object is described by its position vector, r The displacement of the object is defined as the change in its position Δ r = r f - r i
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General Motion Ideas In two- or three-dimensional kinematics, everything is the same as as in one-dimensional motion except that we must now use full vector notation Positive and negative signs are no longer sufficient to determine the direction
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Average Velocity The average velocity is the ratio of the displacement to the time interval for the displacement The direction of the average velocity is the direction of the displacement vector, Δ r t r v
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Instantaneous Velocity The instantaneous velocity is the limit of the average velocity as Δ t approaches zero The direction of the instantaneous velocity is along a line that is tangent to the path of the particle’s direction of motion 0 lim t d t dt   r r v
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Instantaneous Velocity, cont The direction of the instantaneous velocity vector at any point in a particle’s path is along a line tangent to the path at that point and in the direction of motion The magnitude of the instantaneous velocity vector is the speed The speed is a scalar quantity
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Average Acceleration The average acceleration of a particle as it moves is defined as the change in the instantaneous velocity vector divided by the time interval during which that change occurs. f i f i t t t v v v a
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Average Acceleration, cont As a particle moves, Δ v can be found in different ways The average acceleration is a vector quantity directed along Δ v
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Instantaneous Acceleration The instantaneous acceleration is the limit of the average acceleration as Δ v t approaches zero 0 lim t d t dt   v v a
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Producing An Acceleration Various changes in a particle’s motion may produce an acceleration The magnitude of the velocity vector may change The direction of the velocity vector may change Even if the magnitude remains constant Both may change simultaneously
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Kinematic Equations for Two- Dimensional Motion
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CH4 - Chapter 4 Motion in Two Dimensions Motion in Two...

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