Phyf 115 Tutorial 3 44j10

Chapter 3: Vectors ˆ  ˆ    B = 3.00i  − 2.00j , (a) draw the vector sum

1. Two points in the xy plane have Cartesian coordinates (2.00, −4.00) m and (−3.00, 3.00) m. Determine (a) the distance between these points and (b) their polar coordinates.

C = A + B and the vector difference D = A − B. (b) Calculate C and D, first in of unit vectors and then in of polar coordinates, with angles measured with respect to the +x axis.

2. If the rectangular coordinates of a point are given by (2, y) and its polar coordinates are (r, 30°), determine y and r. 3. Vector A has a magnitude of 8.00 units and makes an angle of 45.0° with the positive x axis. Vector B also has a magnitude of 8.00 units and is directed along the negative x axis. Using graphical methods, find (a) the vector sum A + B and (b) the vector difference A − B.

6. Vector A has x and y components of −8.70 cm and 15.0 cm, respectively; vector B has x and y components of 13.2 cm and −6.60 cm, respectively. If A − B + 3C = 0, what are the components of C? 7. An airplane starting from airport A flies 300 km east, then 350 km at 30.0° west of north, and then 150 km north to arrive finally at airport B. (a) The next day, another plane flies directly from A to B in a straight line. In what direction should the pilot travel in this direct flight? (b) How far will the pilot travel in this direct flight? Assume there is no wind during these flights.

4. Each of the displacement vectors A and B shown in Fig. P3.15 has a magnitude of 3.00 m. Find graphically (a) A + B, (b) A − B, (c) B − A, (d) A − 2B. Report all angles counterclockwise from the positive x axis.

8. Two vectors A and B have precisely equal magnitudes. In order for the magnitude of A + B to be one hundred times larger than the magnitude of A – B, what must be the angle between them? 9. A vector is given by R =

2ˆi + ˆj + 3kˆ . Find

(a) the magnitudes of the x, y, z components, (b) the magnitude of R, and (c) the angles between R and the x, y, and z axes. 10. An air-traffic controller observes two aircraft on his radar screen. The first is at altitude 800 m, horizontal distance 19.2 km, and 25.0° south of west. The second aircraft is at altitude 1 100 m, horizontal distance 17.6 km, and 20.0° south of west. What is the distance between the two aircraft? (Place the x axis west, the y axis south, and the z axis vertical.) Fig P3.15

11. A person going for a walk follows the path shown in Fig. P3.59. The total trip consists of four straight-line paths. At the end of the walk, what is the person's resultant displacement measured from the starting point?

Fig

3.59 5. Given the vectors   A = 2.00 ˆ  i  + 6.00ˆ  j  and 1

12. Vectors A and B have equal magnitudes of 5.00. If the sum of A and B is the vector determine the angle between A and B.

ˆ    6.00j ,

2