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- Check Your Understanding Verify that vector v V obtained in Example 2.14 is indeed a unit vector by computing its magnitude. If the convoy in Example 2.8 was moving across a desert flatland—that is, it the third component of its velocity was zero—what is the unit vector of its direction of motion? Which geographic direction does it represent?A small plane flies at 200 km/h in still air. If the wind blows directly out of the west at 50 km/h, (a) in what direction must the pilot head her plane to move directly north across land and (b) how long does it take her to reach a point 300 km directly north of her starting point?Check your Understanding A cyclist rides 3 km west and then tune around and tides 2 kin east. (a) What Is his displacement? (b) What is the distance traveled? (c) What is the magnitude of his displacement?
- A trapper walks a 5.0-lan straight-line distance from her cabin to the lake, as shown in the following figure. Determine the east and north components of her displacement vector. How many more kilometers would she have to walk if she walked along the component displacements? What is her displacement vector?IT.0.0a Given an acceleration vector, initial velocity (uo.Vo), and initial position {xo.yo}, find the velocity and position vectors for t2 0. a(t) = (cos t,5 sin t. (Uo Vo) = (0,5) , (Xo.Yo) = (2.0) What is the velc | vector? v(t) =In the sport of billiards, event organizers often remove one of the rails on a pool table to allow players to measure the speed of their break shots (the opening shot of a game in which the player strikes a ball with his pool cue). V. o h d The top of a pool table is a height h = 3.25 ft from the floor. If a player's ball lands a distance d 14.75 ft from the table edge, what is her break shot speed vo? 12.3 Vo = mph Incorrect At what speed v did her pool ball hit the ground? 4.21 mph = Incorrect
- The position of a particle is given by r(f) = Acos(wt)i + Asin(wt)j + ctk, where A is a constant with units of meters, w is a constant with units of rad/s. and c is a constant with units of m/s. What is the velocity vector?| What is the acceleration vector?A plane flies with the Jet Stream (tailwind) from Chicago to Rome in 9.1 hours, a flight distance of 7740 km. It returns, flying against the Jet Stream (headwind), in 10.8 hours. Calculate the average speed of the plane and the average speed of the wind. Must list assumptions, and draw 1D vector diagram!!! wr Mnments Question 2 ssions The acceleration vector is tangent to the hodograph. O True O False Dus omes zes Question 3
- A particle undergoes three consecutive displacements: and d3 = (-- 13i + 15j) cm. Find the components of the Solution Three-dimensional displacements are more diffi- + 12k) cm, d, = (23i – 14j -5.0k) cm Your final p (15i + 30j d = the origin. Despite sions, we ca resultant displacement and its magnitude. to the care for vector cult to imagine than those in two dimensions, because the latter can be drawn on paper. For this problem, let us conceb tualize that you start with your pencil at the origin of a piece of graph paper on which you have drawn x and y axes. Move your pencil 15 cm to the right along the x axis, then 30 cm upward along the y axis, and then 12 cm vertically away from the graph paper. This provides the displacement described by dj. From this point, move your pencil 23 cm to the right parallel to the x axis, 14 cm parallel to the graph paper in the -y direction, and then 5.0 cm vertically downward to- ward the graph paper. You are now at the displacement from the origin…Question 4: A particle is thrown into air with initial speed vo making angle 0 with the horizontal as shown in Figure 1. The gravitational acceleration g and a constant acceleration a, due to a wind act on the particle. Find the range of the motion. a, 'w Figure 1 100A body moves in space , the location vector r 2 = 2t i +tj +2 k m, How much the velocity of it at 2 second V = m/sec (2 aic aïcw ya ps ?) ثانيه Select one: a. 10.05 mls b. 8.06 m/s c. 9.03 m/s d. 7.02 m/s