Problem 2.1CYU: Check Your Understanding Two motorboats named Alice and Bob are moving on a lake. Given the... Problem 2.2CYU: Check Your Understanding A cave diver enters a tong underwater tunnel. When her displacement with... Problem 2.3CYU: Check Your understanding Using the three displacement vectors A , B , and F in Figure 2.13, choose a... Problem 2.4CYU: Check your Understanding A blue fly lands on a sheet of graph paper a point located 10.0 cm to the... Problem 2.5CYU: Check Your Understanding If the displacement vector of a blue fly walking on a sheet of graph paper... Problem 2.6CYU: Check Your Understanding If Trooper runs 20 m west before taking a rest, what is his displacement... Problem 2.7CYU: Check Your Understanding If the average velocity vector of the drone In the displacement in Example... Problem 2.8CYU: Check Your understanding Three displacement vectors A , B , and F in (Figure 2.13) are specified by... Problem 2.9CYU: Check Your Understanding Suppose that Balto in Example 2.10 leaves the game to attend to more... Problem 2.10CYU: Check Your Understanding Verify that vector v V obtained in Example 2.14 is indeed a unit vector by... Problem 2.11CYU: Check Your Understanding For the vectors given in Figure 2.13, find the scalar products AB and FC .... Problem 2.12CYU: Check Your Understanding For vector in a rectangular coordinate system, use Equation 2.29 through... Problem 2.13CYU: Check Your Understanding Find the angle between forces F1and F3in Example 2.16. Problem 2.14CYU: Check Your Understanding How much work is done by the first dog and by the second dog In Example... Problem 2.15CYU: Check Your Understanding For the vectors given in Figure 2.13, find the scalar products AB and CF .... Problem 2.16CYU: Check Your Understanding Given two vectors and , find (a) (b) (c) the angle between and , and (d)... Problem 1CQ: Scalars and Vectors A weather forecast states the temperature is predicted to be 5Cthe following... Problem 2CQ: Which of the following is a vector a person’s height, the altitude on Mt. Everest, the velocity of a... Problem 3CQ: Give a specific example of a vector, stating its magnitude, units, and direction. Problem 4CQ: What do vectors and scalars have in common? How do they differ? Problem 5CQ: Suppose you add two vectors A and B . What relative direction between them produces the resultant... Problem 6CQ: Is it possible to add a scalar quantity to a vector quantity? Problem 7CQ: Is it possible for two vectors of different magnitudes to add to zero? Is it possible for three... Problem 8CQ: Does the odometer in an automobile indicate a scalar or a vector quantity? Problem 9CQ: When a 10,000-rn runner competing on a 400-rn track crosses the finish line, what is the runner’s... Problem 10CQ: A vector has zero magnitude. Is it necessary to specify its direction? Explain. Problem 11CQ: Can a magnitude of a vector be negative? Problem 12CQ: Can the magnitude of a particle’s displacement be greater that the distance traveled? Problem 13CQ: If two vectors are equal, what can you say about their components? What can you say about their... Problem 14CQ: If three vectors sum up to zero, si1at geometric condition do they satisfy? Problem 15CQ: Give an example of a nonzero vector that has a component of zero. Problem 16CQ: Explain why a vector cannot have a component greater than its own magnitude. Problem 17CQ: If two vectors are equal, what can you say about their components? Problem 18CQ: If vectors A and B are orthogonal, what is the component of B along the direction of A ? What Is the... Problem 19CQ: If one of the two components of a vector is not zero, can the magnitude of the other vector... Problem 20CQ: If two vectors have the same magnitude, do their components have to be the same? Problem 21CQ: What is wrong with the following expressions? How can you correct them? (a) C=AB , (b) C=AB , (c)... Problem 22CQ: If the cross product of two vectors vanishes, what can you say about their directions? Problem 23CQ: If the dot product of two vectors vanishes, what can you say about their directions? Problem 24CQ: What is the dot product of a vector with the cross product that this vector has with another vector? Problem 25P: A scuba diver makes a slow descent into the depths of the ocean. His vertical position with respect... Problem 26P: In a tug-of-war game on one campus, 15 students pull on a rope at both ends in an effort to displace... Problem 27P: Suppose you walk 18.0 m straight west and then 25.0 m straight north. How far are you from your... Problem 28P: For the vectors given in the following figure, use a graphical method to find the following... Problem 29P: A delivery man starts at the post office, chives 40 km north, then 20 km west, then 60 km northeast,... Problem 30P: An adventurous dog strays from home, runs three blocks east, two blocks north, one block east, two... Problem 31P: In an attempt to escape a desert island, a castaway builds a raft and sets out to sea. The wind... Problem 32P: A small plane flies 40.0 km in a direction 60 north of east and then files 30.0 km in a direction 15... Problem 33P: A trapper walks a 5.0-km straigt4ine distance from his cabin to the lake, as shown in the following... Problem 34P: A surveyor measures the distance across a river that flows straight north by the following method.... Problem 35P: A pedestrian walks 6.0 km east and then 13.0 km north. Use a graphical method to find the... Problem 36P: The magnitudes of two displacement vectors are A=20mand B=6m . What are the largest and the smallest... Problem 37P: Assuming the +x -axis is horizontal and points to the tight, resolve the vectors given In the... Problem 38P: Suppose you walk 18.0 m straight west and then 25.0 m straight north. How far are you from your... Problem 39P: You drive 7.50 km in a straight line in a direction 15 east of north. (a) Find the distance you... Problem 40P: A sledge is being pulled by two horses on a flat terrain. The net force on the sledge can be... Problem 41P: A trapper walks a 5.0-lan straight-line distance from her cabin to the lake, as shown in the... Problem 42P: The polar coordinates of a point are 4/3and 5.50 m. What are its Cartesian coordinates? Problem 43P: Two points in a plane have polar coordinates P1(2.500m,/6) and P2(3.800m,2/3). Determine their... Problem 44P: A chameleon is resting quietly on a lanai screen, waiting for an insect to come by. Assume the... Problem 45P: Two points in the Cartesian plane are A(2.00m,4.00m) and B(-3.00m,3.00m) . Find the distance between... Problem 46P: A fly enters through an open window and zooms around the room. In a Cartesian coordinate system with... Problem 47P: For vectors and , calculate (a) and its magnitude and direction angle, and (b) and its magnitude and... Problem 48P: A particle undergoes three consecutive displacements given by vectors , and . (a) Find the resultant... Problem 49P: Given two displacement vectors A=(3.00i-4.00j-4.00K)m and B=(2.00i+3.00j-7.00K)m , find the... Problem 50P: A small plane flies 40.0 km ma direction 60 north of east and then flies 30.0 km in a direction 15... Problem 51P: In an attempt to escape a desert island, a castaway builds a raft and sets out to sea. The wind... Problem 52P: Assuming the +x -axis is horizontal to the right for the vectors given in the following figure, use... Problem 53P: Given the vectors in the preceding figure, find vector Rthat solves equations (a) D+R=Fand (b)... Problem 54P: A delivery man starts at the post office, drives 40 km north, then 20 km west, then 60 km northeast,... Problem 55P: An adventurous dog strays from home, runs three blocks east, two blocks north, and one block east,... Problem 56P: If , and , find the unknown constants a and b such that . Problem 57P: Given the displacement vector , find the displacement vector so that . Problem 58P: Find the unit vector of direction for the following vector quantities: (a) Force , displacement ,... Problem 59P: At one point in space, the direction of the electric field vector Is given In the Cartesian system... Problem 60P: A barge is pulled by the two tugboats shown in the following figure. One tugboat pulls on the barge... Problem 61P: In the control tower at a regional airport, an air traffic controller monitors two aircraft as their... Problem 62P: Assuming the axis is horizontal to the right for the vectors in the following figure, find the... Problem 63P: Assuming the +x-axis is horizontal to the right for the vectors in the preceding figure, find (a)... Problem 64P: Find the angle between vectors for (a) D=(-3.0i-4.0j)m and A=(-3.0i+4.0j)m and (b) D=(2.0i+4.0j+K)m... Problem 65P: Find the angles that vector makes with the and axes. Problem 66P: Show that the force vector is orthogonal to the force vector Problem 67P: Assuming the +x-axis is horizontal to the right for the vectors in the previous figure, find the... Problem 68P: Find the cross product for (a) and (b) and (c) and and (d) and Problem 69P: For the vectors in the earlier figure, find (a) (AF)D , (b) (AF)(DB) , and (c) (AF)(DB) . Problem 70P: (a) If AF=BF , can we conclude A=B ? (b) If AF=BF , can we conclude A=B ? (c) If FA=BF , can we... Problem 71AP: You fly 32.0 km in a straight line in still air in the direction 35.0 south of west. (a) Find the... Problem 72AP: Rectangular coordinates of a point are given by (2,y) and its polar coordinates are given by (r,/6)... Problem 73AP: If the polar coordinates of a point are (r,)and its rectangular coordinates are (x,y) , determine... Problem 74AP Problem 75AP: Starting at the island of Moi in an unknown archipelago, a fishing boat makes a round trip with two... Problem 76AP: An air traffic controller notices two signals from two planes on the radar monitor. One plane is at... Problem 77AP: Show that when A+B=C then A2+B2+2ABcos , where is the angle between vectors A and B . Problem 78AP: Four force vectors each have the same magnitude f.What is the largest magnitude the resultant force... Problem 79AP: A skater glides along a circular path of radius 5.00 m in clockwise direction. ‘When he coasts... Problem 80AP: A stubborn dog is being walked on a leash by its owner. At one point, the dog encounters an... Problem 81AP: If the velocity vector of a polar bear is u=(-18.0 i -13.0 j)km/h , how fast and in what geographic... Problem 82AP: Find the scalar components of three-dimensional vectors G and H in the following figure and write... Problem 83AP: A diver explores a shallow reef off the coast of Belize. She initially swims 90.0 m north, makes a... Problem 84AP: A force vector A has x and y components, respectively, of -8.80 units of force and 15.00 units of... Problem 85AP: Vectors A and B are two orthogonal vectors in the xy -plane and they have identical magnitudes. If... Problem 86AP: For the three-dimensional vectors in the following figure, find (a) GH , (b) GH , and (c) GH . Problem 87AP: Show that (BC)A is the volume of the parallelepiped, with edges formed by the three vectors in the... Problem 88CP: Vector B is 5.0 cm long and vector A is 4.0 cm long. Find the angle between these two vectors when... Problem 89CP: What is the component of the force vector G=(3.0 i+4.0 j+10.0 k)N along the force vector H=(1.0... Problem 90CP: The following figure shows a triangle formed by the three vectors A , B , and C . If vector C is... Problem 91CP: between points in a plane do not change when a coordinate system is rotated In other words, the... format_list_bulleted
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