A vector
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Physics for Scientists and Engineers: Foundations and Connections
- A pirate has buried his treasure on an island with five trees located at the points (30.0 m, 20.0 m), (60.0 m, 80.0 m), (10.0 m, 10.0 m), (40.0 m, 30.0 m), and (70.0 m, 60.0 m), all measured relative to some origin, as shown in Figure P1.69. His ships log instructs you to start at tree A and move toward tree B, but to cover only one-half the distance between A and B. Then move toward tree C, covering one-third the distance between your current location and C. Next move toward tree D, covering one-fourth the distance between where you are and D. Finally move toward tree E, covering one-fifth the distance between you and E, stop, and dig. (a) Assume you have correctly determined the order in which the pirate labeled the trees as A, B, C, D, and E as shown in the figure. What are the coordinates of the point where his treasure is buried? (b) What If? What if you do not really know the way the pirate labeled the trees? What would happen to the answer if you rearranged the order of the trees, for instance, to B (30 m, 20 m), A (60 m, 80 m), E (10 m, 10 m), C (40 m, 30 m), and D (70 m, 60 m)? State reasoning to show that the answer does not depend on the order in which the trees are labeled. Figure 1.69arrow_forwardFigure 1.19 shows two vectors lying in the xy-plane. Determine the signs of the x- and y-components of A, B, and A+B.arrow_forwardAfter a ball rolls off the edge of a horizontal table at time t = 0, its velocity as a function of time is given by v=1.2i9.8tj where v is in meters per second and t is in seconds. The balls displacement away from the edge of the table, during the time interval of 0.380 s for which the ball is in flight, is given by r=00.3803vdt To perform the integral, you can use the calculus theorem [A+Bf(x)]dx=Adx+Bf(x)dx You can think of the units and unit vectors as constants, represented by A and B. Perform the integration to calculate the displacement of the ball from the edge of the table at 0.380 s.arrow_forward
- For what values of a are the vectors A = 2ai − 2j + ak and B = ai + 2aj + 2k perpendicular?arrow_forwardWhat is the component of the force vector G = (3.0i + 4.0j + 10.0k )N along the force vector H = (1.0i + 4.0j )N ?arrow_forward1. The cross product of j x i isa. 0 b.1 c. –k d. -1 2. An airplane travels 200 miles due west and then 150 miles 600 north of west. What isthe resultant?a. 304.1 mi NE b. 304.1 mi SE c. 304.1 mi WS d. 304.1 mi NWarrow_forward
- Given the displacement vectors A → = ( 3 i ^ − 4 j ^ + 4 k ^ ) m and B → = ( 2 i ^ + 3 j ^ − 7 k ^ ) m , find the magnitudes of the following vectors and express each in terms of its rectangular components. (a) C → = A → + B → (b) D → = 2 A → − B →arrow_forwardA rabbit runs across a parking lot on which a set of coordinate axes has, strangely enough, been drawn. The coordinates (meters) of the rabbit’s position as functions of time t (seconds) are given by x=-0.31t2 + 7.2t + 28 (4-5) and y =0.22t2 - 9.1t + 30. (4-6) (a) At t = 15 s, what is the rabbit’s position vector in unitvector notation and in magnitude-angle notation?arrow_forwardFind the unit vector ˆeD in the direction of vector D~ = 1/2 ˆı +ˆj + 2/3 ˆk . (a) 1/√ 61 3ˆı + 6ˆj + 4ˆk (b) 1/√ 46 ˆı − 3ˆj + 6ˆk (c) 1/√ 209 12ˆı +ˆj − 8 ˆk (d) 1/√ 21 2ˆı − 4ˆj + ˆk (e) 1/√ 83 ˆı +ˆj − 9arrow_forward
- Show that the force vectorD ⃗ = (2.0i ^ − 4.0j ^ +k ^ )N is orthogonal to the force vector G ⃗ = (3.0i ^ + 4.0j ^ + 10.0k ^ )N .arrow_forwardGiven the displacement vectors A = (2i + 4j + 4k) m and B = (5i - 2j + 3k) m, findthe magnitudes of the vectors; a) C= A+2B and b) D= 2A - B, also expressing each interms of its x, y, and z components.arrow_forwardGiven two vectors, Land D where L=275ⅈ-64j and D=161.7ⅈ+44j what is the resultant, R, of these two vectors in i, j, k format? Of course, the k component equals zero in this example. What is the magnitude of the Resultant, or R ? What is the direction of the Resultant, R in the standard two-dimensional x-y plane with respect to the positive x axis?arrow_forward
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