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M Mat x + Lab 2-D PDF file_ X Assigned Topic: M Launch N I How wol Q What is Q Quora | W7.3 Hom Ask a ne How to + c File C:/Users/Arash%20Shakib/Downloads/Documents/file_5.pdf : 17 of 124 o + (L Page view LAN Read aloud A 19 74 Chapter 3 Vectors student has learned that a single equation cannot be solved to determine values for more than one unknown in it. How would you explain to him that both a and b can be determined from the single equation used in part (a)? B and direction of , = 60.0°. The person on the left pulls with a force F, of magni- tude 80.0 N and direction of 6. = 75.0°. Find (a) the sin- gle force that is equivalent F. F to the two forces shown and (b) the force that a third per 89 son would have to exert on the mule to make the resul- tant force equal to zero. The forces are measured in units of newtons (symbolized N). 30. In a game of American foot- Figure P3.29 ball, a quarterback takes the ball from the line of scrim- mage, runs backward a distance of 10.0 yards, and then runs sideways parallel to the line of scrimmage for 15.0 yards. At this point, he throws a forward pass downfield 50.0 yards perpendicular to the line of scrimmage. What is the magnitude of the football’s resultant displacement? 31. Consider the three displacement vectors À = W (3î – 3j)m, B = (i – 4j)m, and c = (-2î + 5j) m. Use the component method to determine (4) the magnitude and direction of D = A + B + C and (b) the magnitude and direction of Ē = – A – B + C. 32. Vector Á has x and y components of -8.70 cm and w 15.0 cm, respectively: vector B has x and y com- ponents of 13,2 cm and -6.60 cm, respectively. If A – B + 3C – 0, what are the components of Ć? 28 The vecto momente. 9.00 : 38. Three displacement vectors of a cro- quet ball are shown in Figure P3.38, where A = 20.0 units, B = 40.0 units, and C| = 30.0 units. Find (a) the resultant in unit- 45.0° vector notation and (b) the magni- 145.0 tude and direction of the resultant displacement. 39. A man pushing a mop across a floor M causes it to undergo two displace- Figure P3.38 ments. The first has a magnitude of 150 cm and makes an angle of 120° with the positive x axis. The resultant displacement has a magnitude of 140 cm and is directed at an angle of 35.0° to the posi- tive x axis. Find the magnitude and direction of the second displacement 40. Figure P3.40 illustrates typical proportions of male (m) and female (f) anatomies. The displacements àm and d from the soles of the feet to the navel have mag- nitudes of 104 cm and 84.0 cm, respectively. The dis- placements demand de from the navel to outstretched fingertips have magnitudes of 100 cm and 86.0 cm, respectively. Find the vector sum of these displacements d, = d. + d, for both people. Type here to search 97% 77°F Mostly sunny 11:18 AM 9/15/2021 M Mat X + Lab 2-DPDF file_x Assigned Topic: M Launch How wo Q What is Q Quora W 7.3 Hom Ask a ne How to + File C:/Users/Arash%20Shakib/Downloads/Documents/file_5.pdf 17 佐 : c Q 18 of 124 + 3 A 19 vector leading from you to the airplane is P = (8.04 X 10’i + 7.60 X 10’j) m as suggested in Figure P3.45. Determine the magnitude and orienta- tion of the airplane’s position vector at t = 45.0 s. Р (D Page view A Read aloud spracements at U and U represent waves on road- ways in the city that are at these angles to the main east-west and north-south streets. (a) Draw a map of the successive displacements. (b) What total distance did she travel? (c) Compute the magnitude and direc- tion of her total displacement. The logical structure of this problem and of several problems in later chapters was suggested by Alan Van Heuvelen and David Malo- ney, American Journal of Physics 67(3) 252-256, March 1999. 50. A jet airliner, moving initially at 300 mi/h to the east, suddenly enters a region where the wind is blowing at 100 mi/h toward the direction 30.0° north of east. What are the new speed and direction of the aircraft relative to the ground? 51. A person going for a walk follows the path shown in M Figure P3.51. The total trip consists of four straight- line paths. At the end of the walk, what is the person’s resultant displacement measured from the starting point? Start 100 m Figure P3.45 46. In Figure P3.46, the line seg. (16.12) ment represents a path from the point with position vector (5i + 3j) m to the point with location (16i + 12j) m. Point (5.3) is along this path, a fraction / of the way to the destination. (a) Find the position vector of Figure P3.46 Point point in terms of f. (b) Evalu- is a fraction fof the ate the expression from part distance from the ini- (a) for f= 0. (c) Explain whether tial point (5, 3) to the the result in part is reason- final point (16, 12). able. (d) Evaluate the expres- sion for f= 1. (e) Explain whether the result in part (d) is reasonable. 47. In an assembly operation illustrated in Figure P3.47, a robot moves an object first straight upward and then also to the east, around an arc forming one-quarter of a circle of radius 4.80 cm that lies in an east-west vertical plane. The robot then moves the object upward and to the north, through one-quarter of a 300 m End 200 m 60.0 150 m 30.0 30.07 Figure P3.51 52. Find the horizontal and vertical components of the 100-m displacement of a superhero who flies from the Type here to search | 0 im 97% 77°F Mostly sunny 11:22 AM 9/15/2021

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