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# Section 4 Motion in Two and Three Dimensions .

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What is Physics?. Position and Displacement. Position vector: . Relocation : . Case 1:
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﻿Section 4 Motion in Two and Three Dimensions 4.1. What is Physics?       4.2. Position and Displacement       4.3. Normal Velocity and Instantaneous Velocity       4.4. Normal Acceleration and Instantaneous Acceleration       4.5. Shot Motion       4.6. Shot Motion Analyzed       4.7. Uniform Circular Motion       4.8. Relative Motion in One Dimension       4.9. Relative Motion in Two Dimensions

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What is Physics?

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Position and Displacement Position vector: Displacement :

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EXAMPLE 1 : Displacement In Fig., the position vector for a molecule is at first at and after that later is What is the molecule\'s dislodging from to ?

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Problem 2 A rabbit keeps running over a parking garage on which an arrangement of organize tomahawks has, for some odd reason, been drawn. The directions of the rabbit\'s position as elements of time t (second) are given by At t=15 s, what is the rabbit\'s position vector in unit-vector documentation and in size point documentation?

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Average and Instantaneous Velocity Instantaneous speed is:

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Particle\'s Path versus Velocity Displacement: The speed vector The bearing of the quick speed of a molecule is dependably digression to the molecule\'s way at the molecule\'s position.

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Problem 3 A rabbit keeps running over a parking garage on which an arrangement of facilitate tomahawks has, for some odd reason, been drawn. The directions of the rabbit\'s position as elements of time t (second) are given by At t=15 s, what is the rabbit\'s speed vector in unit-vector documentation and in extent edge documentation?

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Average and Instantaneous Acceleration Average increasing speed is I nstantaneous quickening is

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Speed up or back off If the speed and increasing speed segments along a given pivot have a similar sign then they are in a similar heading. For this situation, the question will accelerate . On the off chance that the quickening and speed segments have inverse signs , then they are in inverse bearings. Under these conditions, the question will back off .

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Problem 4 A rabbit keeps running over a parking garage on which an arrangement of organize tomahawks has, for some odd reason, been drawn. The directions of the rabbit\'s position as elements of time t (second) are given by At t=15 s, what is the rabbit\'s speeding up vector in unit-vector documentation and in size point documentation?

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How to tackle two-dimensional movement issue? One ball is discharged from rest at a similar moment that another ball is shot evenly to the privilege The level and vertical movements (at right points to each other) are autonomous , and the way of such a movement can be found by consolidating its flat and vertical position segments. By Galileo

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Projectile Motion A molecule moves in a vertical plane with some underlying speed however its quickening is dependably the free-fall increasing speed g , which is descending. Such a molecule is known as a shot and its movement is called shot movement .

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Properties of Projectile Motion The Horizontal Motion: no speeding up speed v x stays unaltered from its underlying incentive all through the movement The even range R is most extreme for a dispatch edge of 45° The vertical Motion: Constant increasing speed g speed v y =0 at the most elevated point.

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Check Your Understanding A shot is discharged into the air, and it takes after the explanatory way appeared in the drawing. There is no air resistance. At any moment, the shot has a speed v and an increasing speed a . Which at least one of the drawings couldn\'t speak to the bearings for v and an anytime on the direction?

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Example 4 A Falling Care Package Figure demonstrates a plane moving on a level plane with a steady speed of +115 m/s at an elevation of 1050 m. The headings to one side and upward have been picked as the positive bearings. The plane discharges a "mind bundle" that tumbles to the ground along a bended direction. Disregarding air resistance, (a). decide the time required for the bundle to hit the ground. (b) discover the speed of bundle B and the course of the speed vector just before bundle B hits the ground.

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Example 5 The Height of a Kickoff A placekicker kicks a football at a point of θ =40.0 o over the even pivot, as Figure shows. The underlying rate of the ball is (an) Ignore air resistance and locate the greatest stature H that the ball achieves. (b) Determine the season of flight amongst kickoff and landing. (c). Compute the range R of the shot.

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UNIFORM CIRCULAR MOTION Uniform roundabout movement is the movement of a question going at a steady (uniform) speed on a round way

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Properties of UNIFORM CIRCULAR MOTION Period of the movement T : is the ideal opportunity for a molecule to circumvent a shut way precisely once has a unique name. Normal speed is : This number of upheavals in a given time is known as the recurrence , f .

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Example 6 A Tire-Balancing Machine The wheel of an auto has a sweep of r =0.29 m and is being turned at 830 cycles for every moment (rpm) on a tire-adjusting machine. Decide the speed (in m/s) at which the external edge of the wheel is moving.

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CENTRIPETAL ACCELERATION Magnitude : The centripetal increasing speed of a question moving with a speed v on a roundabout way of span r has an extent a c given by Direction: The centripetal quickening vector dependably indicates the focal point of the circle and constantly alters course as the protest moves.

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Check Your Understanding The auto in the drawing is moving clockwise around a round area of street at a steady speed. What are the bearings of its speed and increasing speed at taking after positions? Determine your reactions as north, east, south, or west. position 1 position 2

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Example 7 The Effect of Radius on Centripetal Acceleration The coaster track at the 1994 Olympics in Lillehammer, Norway, contained turns with radii of 33 m and 24 m, as Figure represents. Locate the centripetal increasing speed at each turn for a speed of 34 m/s, a speed that was accomplished in the two-man occasion. Express the appropriate responses as products of g=9.8 m/s2.

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Relative Motion in One Dimension The organize The speed The increasing speed

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Relative Motion in Two Dimension The facilitate The speed The quickening

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Sample Problem In Fig. 4-23 a , a plane moves due east while the pilot focuses the plane to some degree south of east, toward a relentless wind that hits toward the upper east. The plane has speed in respect to the twist, with a velocity (speed in respect to the twist) of 215 km/h, coordinated at edge θ south of east. The wind has speed v pG in respect to the ground with speed of 65.0 km/h, coordinated 20.0° east of north. What is the size of the speed of the plane in respect to the ground, and what is θ ?

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