Understanding Two and Three-Dimensional Motion in University Physics

1. University Physics: Mechanics Ch4. TWO- AND THREE-DIMENSIONAL MOTION Lecture 4 Dr.-Ing. Erwin Sitompul http://zitompul.wordpress.com

2. Solution of Homework 3: The Beetles 2nd run, ? 1st run, 1.6 m New location 2nd run, 0.8 m 1st run, 0.5 m Starting point

3. Solution of Homework 3: The Beetles → D → C New location → B → Starting point A Thus, the second run of the green beetle corresponds to the vector

4. N W E S → D Solution of Homework 3: The Beetles (a) The magnitude of the second run? (b) The direction of the second run? The direction of the second run is 79.09° south of due east or 10.91° east of due south.

5. Moving in Two and Three Dimensions • In this chapter we extends the material of the preceding chapters to two and three dimensions. • Position, velocity, and acceleration are again used, but they are now a little more complex because of the extra dimensions.

6. Position and Displacement • One general way of locating a particle is with a position vectorr, → • The coefficients x, z, and y give the particle’s location along the coordinate axes and relative to the origin. • The following figure shows a particle with position vector • In rectangular coordinates, the position is given by (–3 m, 2 m, 5 m).

7. Position and Displacement • As a particle moves, its position vector changes in a way that the vector always extends from the originto the particle. • If the position vector changes from r1to r2, then the particle’s displacement delta is: → →

8. Average Velocity and Instantaneous Velocity → • If a particle moves through a displacement Δrin a time interval Δt, then its average velocityvavg is: → • The equation above can be rewritten in vector components as:

9. Average Velocity and Instantaneous Velocity → • The particle’s instantaneous velocity v is the velocity of the particle at some instant. • The direction of instantaneous velocity of a particle is always tangent to the particle’s path at the particle’s position.

10. Average Velocity and Instantaneous Velocity • Writing the last equation in unit-vector form: • This equation can be simplified by rewriting it as: → where the scalar components of v are: • The next figure shows a velocity vector v and its scalar x and y components. Note that v is tangent to the particle’s path at the particle’s position. → →

11. Average Velocity and Instantaneous Velocity The figure below shows a circular path taken by a particle. If the instantaneous velocity of the particle at a certain time isv = 2i – 2j m/s, through which quadrant is the particle currently moving when it is traveling clockwise (b) counterclockwise ^ ^ → Firstquadrant Thirdquadrant (a) clockwise (b) counterclockwise

12. Homework 4: The Plane A plane flies 483 km west from city A to city B in 45 min and then 966 km south from city B to city C in 1.5 h. From the total trip of the plane, determine: (a) the magnitude of its displacement; (b) the direction of its displacement; (c) the magnitude of its average velocity; (d) the direction of its average velocity; (e) its average speed.

13. Homework 4 A turtle starts moving from its original position with the speed 10 cm/s in the direction 25° north of due east for 1 minute. Afterwards, it continues to move south for 2 m in 8 s. From the total movement of the turtle, determine: (a) the magnitude of its displacement; (b) the direction of its displacement; (c) the magnitude of its average velocity; (d) the direction of its average velocity; (e) its average speed. New