Problem 2. (b) 5 cm. Problem 3. (a) x/ cm, 9 = 33.70, (b) 1, -5. Problem 6. (a) (2.7\": 63)) cm, (b) (457 + 21)) cm, (c) 2m cm, (d) 2M5 cm, (6) -71.56, 26.57. Problem 7. (a) 3.5 km, (b) 2.11 km, 955. Problem 8. 10003} m, 0. Problem 9. 0.82 mile, 33.10 North of West. Problem 10. 0.46 km West and 2.29 km North. PROBLEM SET 1, VECTORS Problem 1. Consider the four vectors in the figure to the right. A Graphically determine the following vectors, R = A + B + C + D, S = 2A - B - 3C + D and T = D - 3C + 2A - B. Problem 2. Let A = 3x cm and B = 4y cm where the cm stands for centimeters. (a) Graphically determine A + B and A - B. D (b) Determine |A + B| and |A - B). The result should make it B C clear that we need to treat these as vectors and not scalars. Problem 3. Let A = (3x + 2y) cm and B = (x + ay) cm. (a) Determine the magnitude and direction of A. Draw this vector on your own set of axes. Figure 1: Vectors for problem 1 (b) If |A + B| = 5 cm, find any possible values for a. Problem 4. Can you find two vectors with different lengths that have a vector sum of zero? Explain your answer. Problem 5. Can the magnitude of an object's displacement be larger than the distance it has traveled? What is the condition for them being equal. Explain your answers.For the rest of the problems you must make a drawing as well as solve the problem with numbers. Problem 6. Two vectors are given by if = (351': 2g) cm and g = (': 433) cm. Calculate (a) A + B, (b) A B, (c) |A + 3|, ((1) |A 3| and (e) the direction of 14 3' and AL 8'. Problem 7. A car drives North for 1 km. Then it turns and drives 2 km at 30 South of West. Finally the driver turns again and drives 0.5 km Northwest. (a) What is the total distance driven? (b) What are the magnitude and direction of the car's overall displacement? Problem 8. A circular track has a radius of 500 m. What is the displacement of a bicyclist when they travel around the track from the north side to the south side? When they make one complete circle around the track? Explain your answers. Problem 9. A jogger runs 1 mile due west, then she changes direction for a second leg of the run. At the end of the run, she is 1.75 miles from the starting point at an angle of 15" north of west. What was the direction and length of the second leg of the run? Problem 10. A lost driver in Tucson drives 3 km north, 2 km northeast, 4 km west, and then 3 km southeast. Where does he end up relative to his starting point