SM_PDF_chapter3

SM_PDF_chapter3 - Motion in Two Dimensions CHAPTER OUTLINE...

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51 Motion in Two Dimensions CHAPTER OUTLINE 3.1 The Position, Velocity, and Acceleration Vectors 3.2 Two-Dimensional Motion with Constant Acceleration 3.3 Projectile Motion 3.4 The Particle in Uniform Circular Motion 3.5 Tangential and Radial Acceleration 3.6 Relative Velocity 3.7 Context Connection Lateral Acceleration of Automobiles ANSWERS TO QUESTIONS Q3.1 No, you cannot determine the instantaneous velocity. Yes, you can determine the average velocity. The points could be widely separated. In this case, you can only determine the average velocity, which is r r v x = t . Q3.2 (a) r v r v r v r v r a r a r a r a FIG. Q3.2(a) (b) r v r v r v r v r a r a r a r a r v r a FIG. Q3.2(b) Q3.3 The easiest way to approach this problem is to determine acceleration first, velocity second and finally position. Determine (c) acceleration first, (b) velocity second, and (a) finally position. Vertical: In free flight, a g y =− . At the top of a projectile’s trajectory, v y = 0. Using this, the maximum height can be found using vv a y y fy iy y f i 22 2 =+ di . Horizontal: a x = 0 , so v x is always the same. To find the horizontal position at maximum height, one needs the flight time, t . Using the vertical information found previously, the flight time can be found using a t fy iy y . The horizontal position is xv t fi x = . If air resistance were taken into account, then the acceleration in both the x and y -directions would have an additional term due to the drag.
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52 Motion in Two Dimensions Q3.4 The balls will be closest together as the second ball is thrown. Yes, the first ball will always be moving faster, since its flight time is larger, and thus the vertical component of the velocity is larger. The time interval will be one second. No, since the vertical component of the motion determines the flight time. Q3.5 A parabola. Q3.6 (a) no (b) yes (c) yes (d) no Q3.7 The projectile is in free fall. Its vertical component of acceleration is the downward acceleration of gravity. Its horizontal component of acceleration is zero. Q3.8 The optimal angle would be less than 45 ° . The longer the projectile is in the air, the more that air resistance will change the components of the velocity. Since the vertical component of the motion determines the flight time, an angle less than 45 ° would increase range. Q3.9 The projectile on the moon would have both the larger range and the greater altitude. Apollo astronauts performed the experiment with golf balls. Q3.10 The racing car rounds the turn at a constant speed of 90 miles per hour. Q3.11 (a) no (b) yes In the second case, the particle is continuously changing the direction of its velocity vector. Q3.12 (a) The velocity is not constant because the object is constantly changing the direction of its motion. (b) The acceleration is not constant because the acceleration always points towards the center of the circle. The magnitude of the acceleration is constant, but not the direction.
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This note was uploaded on 10/18/2008 for the course PHYS 3Q2341234 taught by Professor Dafsf during the Spring '08 term at UCLA.

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SM_PDF_chapter3 - Motion in Two Dimensions CHAPTER OUTLINE...

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