CHAPTER 3

1. (P.95 Prob.28) Let A = (3.0 m, 20° south of east), B = (2.0 m, north), and C = (5.0 m, 70° south of west).
   (a) Draw and label A, B, and C with their tails at the origin. Use a coordinate system with the x-axis to the east.
   (b) Write A, B, and C in component form, using unit vectors.
   (c) Find the magnitude and the direction of D = A + B + C.
2. (P.95 Prob.32) The position of a particle as a function of time is given by r = (5i + 4J)t² m, where t is in second.
   a. what is the particle's distance from the origin at t = 0, 2, and 5 s?
   b. Find an expression for the particle's velocity ad a function of time.
   c. What is the particle's speed at t = 0, 2, and 5 s?
3. (P.95 Prob.36) Jim's dog Sparky runs 50 m northeast to a tree, then 70 m west to a second tree, and finally 20 m south to a third tree.
   a. Draw a picture and establish a coordinate system.
   b. Calculate Sparky's net displacement in component form.
   c. Calculate Sparky's net displacement as a magnitude and an angle.
4. (P.96 Prob.44) A flock of ducks is trying to migrate south for the winter, but they keep being blown off course by a wind blowing from the west at 6.0 m/s. A wise elder duck finally realizes that the solution is to fly at an angle to the wind. If the ducks can fly at 8.0 m/s relative to the air, what direction should they head in order to move directly south?
5. (P.96 Prob.48) Three forces are exerted on an object placed on a tilted floor in figure P3.48. The forces are measured in newtons (N). Assuming that forces are vectors,
   
   a. What is the component of the net force F_net = F₁ + F₂ + F₃ parallel to the floor?
   b. What is the component F_net  perpendicular to the floor?
   c. What are the magnitude and direction of F_net ?