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1、Motion in Two and Three Dimensions,Dr. Huaqiu Deng E-mail: ,Motion in Two and Three Dimens,Position and Displacement,Position vectorRectangular coordinates,Position and DisplacementPosit,Sample Problem,Displacement,Sample Problem Displacement,大学物理英文课件4-Motion-in-Two-and-Three-Dimensions,大学物理英文课件4-Mo
2、tion-in-Two-and-Three-Dimensions,Average and Instantaneous Acceleration,instantaneous acceleration:,Average and Instantaneous Acce,大学物理英文课件4-Motion-in-Two-and-Three-Dimensions,Sample Problem,Problem: A rabbit runs across a parking lot on which a set of coordinate axes has, strangely enough, been dra
3、wn. The coordinates (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 rabbi,Features: the horizontal motion and the vertical motion are independent of each oth
4、er,Projectile Motion,Features: the horizontal motio,Projectile Motion Analyzed,Horizontal Motion: velocity remains constant,The Vertical Motion: as free-fall motion,The Equation of Path,Projectile Motion Analyzed Hor,Projectile Motion Analyzed,The Horizontal Range,Projectile Motion Analyzed The,Samp
5、le Problem,Problem: 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 ca
6、psule reaches the water, 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 Problem,Problem: The figure shows a pirate ship 560m from a fort defending a harbor entrance. A defense cann
7、on, located at sea level, 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 fig,Even constant speed, the velocity changes in direction.,
8、The velocity is always directed tangent to the circle in the direction of motion.,Uniform Circular Motion,The acceleration is always directed radially inward.,Centripetal acceleration,Even constant speed, the veloc,velocity depends on the reference frame,Frame A on the groundFrame B on moving carObj
9、ect P on another car,Relative Motion in One Dimension,velocity depends on the refere,Sample Problem,Problem: 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 = -
10、78 km/h for car P, what velocity 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 th
11、e braking?,Solution:,(a),Sample ProblemProblem: In the,Sample Problem,(b),(c),Sample Problem(b)(c),Relative Motion in Two Dimensions,Relative Motion in Two Dimensi,Sample Problem,Problem: In the figure, a plane moves due east while the pilot points the plane somewhat south of east, toward a steady w
12、ind 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 north. What is the magnitude of the velocity vPG of the plane relative to the ground, and what is ?,Solution:,Sample ProblemProblem: In the,Homework,#10 of P78#20#27#56#69#73,Homework#10 of P78,
