List your collaborators. You need to list at least one classmate as a collaborator or else you will lose 2 points. All angles should be between 0 and 360. Give answers to 3 significant figures unless otherwise instructed. 1. Calculate the dot product A . B of the following pairs of vectors and find the (smaller) angle between the two vectors. (a) A= -3.0i + 6.03 and B = 5.0i - 2.0j. (b) These vectors are in polar coordinates. A = (5 m, 0A = 30) and B = (2 m, 0B = 300). (c) A= -2.02 + 3.03 and B = (4.0, 0B = 150) 2. The dot product of vectors A and B is +48 m2. Vector A has a magnitude of 6.00 m and direction 28.0 West of South. If vector B has direction 39.0 South of East, what is the magnitude of B? 3. Two cars are travelling on intersecting roads. Car A is approaching the inter- section travelling North at a rate of 55 miles per hour, and Car B is approaching the intersection travelling to the West at 70 miles per hour. At time t=0, Car A is 10 miles from the intersection, and Car B is 7.8 miles from the intersection. (a) Taking the intersection of the roads to be your origin, write the positions of each car as a function of time. (b) What is the velocity of Car B relative to Car A? Give your answer in terms of magnitude and direction. (c) Assuming both cars retain their constant velocity, at what time (in hours) do the cars make their closest approach? (Hint: Use a derivative to find the minimum distance.) 4. A powerboat heads due northwest (450 north of west) at 13 m/s relative to the water across a river that flows due north at 5.0 m/s. What is the velocity (both magnitude and direction) of the motorboat relative to the shore? Give your answer to 2 significant figures. 5. According to ground based radar, an airplane is flying 15 degrees north of west at a speed of 100 mph. The weather report states that the wind is blowing in the southeast direction, i.e., 45 degrees south of east, with a speed of 35 mph. What is the airspeed of the plane? In other words, what is the speed of the plane relative to the air? Give your answer to 2 significant figures