《大學物理》英文課件4-Motion-in-Two-and-Three-Dimensions

1、Motion in Two and Three Dimensions Dr. Huaqiu Deng E-mail: Motion in Two and Three DimensPosition and DisplacementPosition vectorRectangular coordinates Position and DisplacementPositSample Problem Displacement Sample Problem Displacement 大學物理英文課件4-Motion-in-Two-and-Three-Dimensions大學物理英文課件4-Motion-

2、in-Two-and-Three-DimensionsAverage and Instantaneous Acceleration instantaneous acceleration: Average and Instantaneous Acce大學物理英文課件4-Motion-in-Two-and-Three-DimensionsSample ProblemProblem: A rabbit runs across a parking lot on which a set of coordinate axes has, strangely enough, been drawn. The c

3、oordinates (meters) of the rabbits position as functions of time t (seconds) are given by x = -0.31t2+7.2t+28, y = 0.22t2 - 9.1t+30. find the velocity at time t =15s.Solution:Sample ProblemProblem: A rabbiFeatures: the horizontal motion and the vertical motion are independent of each other Projectil

4、e MotionFeatures: the horizontal motioProjectile Motion Analyzed Horizontal Motion: velocity remains constantThe Vertical Motion: as free-fall motionThe Equation of PathProjectile Motion Analyzed HorProjectile Motion Analyzed The Horizontal Range Projectile Motion Analyzed TheSample ProblemProblem:

5、In the Figure, a rescue plane flies at 198 km/h (=55.0 m/s) and constant height h=500 m toward a point directly over a victim, where a rescue capsule is to land. (a) What should be the angle of the pilots line of sight to the victim when the capsule release is made? (b) As the capsule reaches the wa

6、ter, what is its velocity in unit-vector notation and in magnitude-angle notation?Solution: (a) Sample ProblemProblem: In the Sample Problem (b) Sample Problem (b) Sample ProblemProblem: The figure shows a pirate ship 560m from a fort defending a harbor entrance. A defense cannon, located at sea lev

7、el, fires balls at initial speed v0= 82 m/s. (a) At what angle 0 from the horizontal must a ball be fired to hit the ship? (b) What is the maximum range of the cannonballs?Solution:(a) (b) Sample ProblemProblem: The figEven constant speed, the velocity changes in direction.The velocity is always dir

8、ected tangent to the circle in the direction of motion. Uniform Circular MotionThe acceleration is always directed radially inward. Centripetal accelerationEven constant speed, the velocvelocity depends on the reference frame Frame A on the groundFrame B on moving carObject P on another carRelative

9、Motion in One Dimensionvelocity depends on the refereSample ProblemProblem: In the figure, suppose that Barbaras velocity relative to Alex is a constant vBA = 52 km/h and car P is moving in the negative direction of the x axis. (a) If Alex measures a constant vPA = -78 km/h for car P, what velocity

10、vPB will Barbara measure? (b) If car P brakes to a stop relative to Alex (and thus relative to the ground) in time t = 10 s at constant acceleration,what is its acceleration aPA relative to Alex? (c) What is the acceleration aPB of car P relative to Barbara during the braking?Solution:(a)Sample Prob

11、lemProblem: In the Sample Problem(b)(c)Sample Problem(b)(c)Relative Motion in Two Dimensions Relative Motion in Two DimensiSample ProblemProblem: In the figure, a plane moves due east while the pilot points the plane somewhat south of east, toward a steady wind that blows to the northeast. The plane has velocity vPW relative to the wind, with an airspeed (speed relative to the wind) of 215 km/h, directed at angle south of east. The wind has velocity vWG relative to the ground with speed 65.0 km/h, directed 20.0 east of nort