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Unformatted text preview: 4 Motion in Two Dimensions CHAPTER OUTLINE 4.1 The Position, Velocity, and Acceleration Vectors 4.2 Two-Dimensional Motion with Constant Acceleration 4.3 Projectile Motion 4.4 Uniform Circular Motion 4.5 Tangential and Radial Acceleration 4.6 Relative Velocity and Relative Acceleration ANSWERS TO QUESTIONS * Q4.1 The cars acceleration must have an inward component and a forward component: answer (f ). Another argument: Draw a fi nal velocity vector of two units west. Add to it a vector of one unit south. This represents subtracting the initial velocity from the fi nal velocity, on the way to fi nding the acceleration. The direction of the resultant is that of vector (f ). Q4.2 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 avg t = x 65 Q4.3 (a) (b) *Q4.4 (i) The 45 angle means that at point A the horizontal and vertical velocity components are equal. The horizontal velocity component is the same at A, B , and C . The vertical velocity component is zero at B and negative at C . The assembled answer is a = b = c = e > d = 0 > f (ii) The x-component of acceleration is everywhere zero and the y-component is everywhere 9.8 m / s 2 . Then we have a = c = e = 0 > b = d = f. Q4.5 A parabola results, because the originally forward velocity component stays constant and the rocket motor gives the spacecraft constant acceleration in a perpendicular direction. Q4.6 (a) yes (b) no: the escaping jet exhaust exerts an extra force on the plane. (c) no (d) yes (e) no: the stone is only a few times more dense than water, so friction is a signifi cant force on the stone. The answer is (a) and (d). Q4.7 The projectile is in free fall. Its vertical component of acceleration is the downward acceleration of gravity. Its horizontal component of acceleration is zero. Q4.8 (a) no (b) yes (c) yes (d) no. Answer: (b) and (c) *Q4.9 The projectile on the moon is in ight for a time interval six times larger, with the same range of vertical speeds and with the same constant horizontal speed as on Earth. Then (i) its range is (d) six times larger and (ii) its maximum altitude is (d) six times larger. Apollo astronauts performed the experiment with golf balls. 13794_04_ch04_p065-092.indd 65 13794_04_ch04_p065-092.indd 65 11/28/06 1:16:09 PM 11/28/06 1:16:09 PM Q4.10 (a) no. Its velocity is constant in magnitude and direction. (b) yes. The particle is continuously changing the direction of its velocity vector. Q4.11 (a) straight ahead (b) either in a circle or straight ahead. The acceleration magnitude can be constant either with a nonzero or with a zero value....
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