m S 4. A small object moves along the x-axis with acceleration ax(t) = (0.06 3) (t 20.0.9). At t = 05 the object is at x = 10m and has velocity UM = 2 33. a. What is the x-coordinate of the object when t= 10.0 s? b. What is the average velocity from 5 to 10 seconds? 5. A car and a truck start from rest at the same instant, with the car initially at some distance behind the truck. The truck has a constant acceleration of 2.00 m/s2 and the car an acceleration of 4.00 m/sz. The automobile overtakes the truck after the truck has moved 100.0 m. a. How far was the car behind the truck initially? b. What is the velocity of the car when it overtakes the truck? 2. You are given vectors fl. = 53 4] and B" = 31' 6}\". A third vector 5, lies in the xy plane. Vector E is perpendicular to vector 1'3, and the scalar product of 5 with E\" is 20. From this information, find the components of vector 5. 3. Let vectors X =(1,4,1),F = (1,-1,-3), and f = (3,1,1). a. Calculate B - (A) x ) b. Determine/l. X (EX if?) 8. Canada geese migrate essentially along a north-south direction for well over a thousand kilometers in some cases, traveling at speeds up to about 100 km/h. The one goose is ying at 100 km/h relative to the air but a 60 km/h wind is blowing from east to west. a. At what angle relative to the north-south direction should this bird head to travel directly southward relative to the ground? b. How long will it take the goose to cover a ground distance of 400 km from north to south? 9. Three forces, F1) , F2: and F3 act at a point. The magnitude of F1 is 9.00 N, and its direction is an angle 60.0\" above the negative direction of x-axis in the second quadrant. The magnitude of F2. is 6.00 N, and its direction is an angle 45.0" below the negative direction of xaxis in the third quadrant. The magnitude of F3 is 3.00 N, and its direction is an angle 30.00 below the positive direction of xaxis in the fourth quadrant. Determine the magnitude and direction of the equilibrant force (i.e equal in magnitude but opposite to the resultant force). 6. The coordinates of a bird flying in the xy plane are given by x(t) = (4 m/s)t and y(t) = 10.0m (Em/52W. Calculate the magnitude and direction of the bird's velocity at t = 2.0 s. 7. On level ground a shell is fired with an initial velocity of 39.2 m/s at 30" above the horizontal and feels no appreciable air resistance. a. Find half of its maximum height above the ground. b. How far from its firing point does the shell land? 12. As shown in the figure, block A (mass 2.5 kg ) rests on a tabletop. A horizontal cord passing over a light, frictionless pulley to a hanging block B (mass 1.5 kg) connects it. The coefficient of kinetic friction between block A and the tabletop is 0.35. A l? 5\" Draw the free-body diagram for block A and block B. b. After the blocks are released from rest, find the speed (in m/s) of each block after moving 4.00 cm. c. After the blocks are released from rest, find the tension in the cord. 10. A 0.22 caliber rifle bullet traveling at 350 m/s, strikes a large tree and penetrates it to a depth of 0.150 m. The mass of the bullet is 1.50 g. Assume a constant retarding force. a. How much time is required for the bullet to stop? b. What force, in newtons, does the tree exert on the bullet? 11. Assume a Ferris wheel with a diameter of 150 m makes two revolutions every two minutes. a. A passenger weighs 882 N at the weight-guessing booth on the ground. What is his apparent weight at the lowest point on the Ferris wheel? b. What is his apparent weight at the highest point on the Ferris wheel? C. What would be the time for one revolution if the passenger's apparent weight at the highest point were zero? _. 1. You are given two vectors A = 33 4j, = Zi + 3f. a. What is the angle 6 between 15 and 157 ? b. What angle 6C does 5 makes with +7: axis? Assume E = E A