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MATH1720HomeworkChapter7Section4

Multiple Choice
Identify the choice that best completes the statement or answers the question.
 

 1. 
Draw a sketch to represent the vector. Refer to the vectors pictured here.
      mc001-1.jpg
3d
a.
mc001-2.jpg
b.
mc001-3.jpg
 

 2. 
Draw a sketch to represent the vector. Refer to the vectors pictured here.
      mc002-1.jpg
 -b
a.
mc002-2.jpg
b.
mc002-3.jpg
 

 3. 
Draw a sketch to represent the vector. Refer to the vectors pictured here.
      mc003-1.jpg
c + d
a.
mc003-2.jpg
b.
mc003-3.jpg
 

 4. 
Draw a sketch to represent the vector. Refer to the vectors pictured here.
      mc004-1.jpg
 b + c
a.
mc004-2.jpg
b.
mc004-3.jpg
 

 5. 
Draw a sketch to represent the vector. Refer to the vectors pictured here.
      mc005-1.jpg
b - c
a.
mc005-2.jpg
b.
mc005-3.jpg
 

 6. 
Draw a sketch to represent the vector. Refer to the vectors pictured here.
      mc006-1.jpg
d - a
a.
mc006-2.jpg
b.
mc006-3.jpg
 

 7. 
Draw a sketch to represent the vector. Refer to the vectors pictured here.
      mc007-1.jpg
c - d
a.
mc007-2.jpg
b.
mc007-3.jpg
 

 8. 
Draw a sketch to represent the vector. Refer to the vectors pictured here.
      mc008-1.jpg
mc008-2.jpga
a.
mc008-3.jpg
b.
mc008-4.jpg
 

 9. 
Draw a sketch to represent the vector. Refer to the vectors pictured here.
      mc009-1.jpg
a + (c + d)
a.
mc009-2.jpg
b.
mc009-3.jpg
 

 10. 
Draw a sketch to represent the vector. Refer to the vectors pictured here.
      mc010-1.jpg
 a + d
a.
mc010-2.jpg
b.
mc010-3.jpg
 

 11. 
Sketch the vectors u and w with angle è between them and sketch the resultant.
 mc011-1.jpg = 5, mc011-2.jpg = 5, è = 45°
a.
mc011-3.jpg
b.
mc011-4.jpg
 

 12. 
Sketch the vectors u and w with angle è between them and sketch the resultant.
 mc012-1.jpg = 10, mc012-2.jpg = 4, è = 40°
a.
mc012-3.jpg
b.
mc012-4.jpg
 

 13. 
Sketch the vectors u and w with angle è between them and sketch the resultant.
 mc013-1.jpg = 20, mc013-2.jpg = 50, è = 80°
a.
mc013-3.jpg
b.
mc013-4.jpg
 

 14. 
Sketch the vectors u and w with angle è between them and sketch the resultant.
 mc014-1.jpg = 3, mc014-2.jpg = 12, è = 40°
a.
mc014-3.jpg
b.
mc014-4.jpg
 

 15. 
Sketch the vectors u and w with angle è between them and sketch the resultant.
 mc015-1.jpg = 8, mc015-2.jpg = 16, è = 15°
a.
mc015-3.jpg
b.
mc015-4.jpg
 

 16. 
Sketch the vectors u and w with angle è between them and sketch the resultant.
mc016-1.jpg = 50, mc016-2.jpg = 12, è = 35°
a.
mc016-3.jpg
b.
mc016-4.jpg
 

 17. 
Sketch the vectors u and w with angle è between them and sketch the resultant.
 mc017-1.jpg = 5, mc017-2.jpg = 1, è = 60°
a.
mc017-3.jpg
b.
mc017-4.jpg
 

 18. 
Sketch the vectors u and w with angle è between them and sketch the resultant.
mc018-1.jpg = 2.85, mc018-2.jpg = 2.85, è = 90°
a.
mc018-3.jpg
b.
mc018-4.jpg
 

 19. 
Sketch the vectors u and w with angle è between them and sketch the resultant.
 mc019-1.jpg = 45, mc019-2.jpg = 25, è = 30°
a.
mc019-3.jpg
b.
mc019-4.jpg
 

 20. 
Sketch the vectors u and w with angle è between them and sketch the resultant.
mc020-1.jpg = 8, mc020-2.jpg = 3, è = 80°
a.
mc020-3.jpg
b.
mc020-4.jpg
 

 21. 
Two forces act at a point in the plane.  The angle between the two forces is given.  Find the magnitude of the resultant force.
forces of  46.4 and  60.2 lb, forming an angle of  126.7°
(round to the nearest pound)
a.
9116 lb
c.
95 lb
b.
101 lb
d.
49 lb
 

 22. 
Two forces act at a point in the plane.  The angle between the two forces is given.  Find the magnitude of the resultant force.
 forces of  59 and  81 newtons, forming an angle of 90°
(round to the nearest newton)
a.
4779 newtons
c.
100 newtons
b.
22 newtons
d.
140 newtons
 

 23. 
Use the parallelogram rule to find the magnitude of the resultant force for the two forces shown in the figure. Round to one decimal place.

mc023-1.jpg
a.
146.5 lb
c.
132.7 lb
b.
21,459.5 lb
d.
180.3 lb
 

 24. 
Use the parallelogram rule to find the magnitude of the resultant force for the two forces shown in the figure. Round to one decimal place.
mc024-1.jpg
a.
536.7 lb
c.
298.5 lb
b.
346.6 lb
d.
610.0 lb
 

 25. 
Two forces of  425 newtons and  267 newtons act at a point.  The resultant force is  507 newtons. Find the angle between the forces.
a.
88.7°
c.
91.3°
b.
52.7°
d.
163.7°
 

 26. 
A force of  627 lb is required to pull a boat up a ramp inclined at  23° with the horizontal.  How much does the boat weigh?
a.
2182 lb
c.
1605 lb
b.
604 lb
d.
577 lb
 

 27. 
Starting at point A, a ship sails  48 km on a bearing of  217°, then turns and sails  15 km on a bearing of  280°.  Find the distance of the ship from point A.
a.
63 km
c.
71 km
b.
56 km
d.
8 km
 

 28. 
A plane is heading due south with an airspeed of  245 mph.  A wind from a direction of  53° is blowing at  13 mph.  Find the bearing of the plane.
a.
182°
c.
88°
b.
93°
d.
177°
 

 29. 
Two people are carrying a box.  One person exerts a force of  129 pounds at an angle of  49.4° with the horizontal.  The other person exerts a force of  98 pounds at an angle of  52.4°.  Find the weight of the box.
a.
266 lb
c.
177 lb
b.
227 lb
d.
104 lb
 

 30. 
A pilot wants to fly on a bearing of  62.5°.  By flying due east, he finds that a  51-mph wind, blowing from the south, puts him on course.  Find the ground speed of the plane.
a.
110 mph
c.
221 mph
b.
166 mph
d.
57 mph
 

 31. 
A pilot wants to fly on a bearing of  61.8°.  By flying due east, he finds that a  51-mph wind, blowing from the south, puts him on course.  Find the airspeed of the plane.
a.
143 mph
c.
48 mph
b.
95 mph
d.
108 mph
 

 32. 
Suppose you would like to cross a  219-foot wide river in a boat.  Assume that the boat can travel  38 mph relative to the water and that the current is flowing west at the rate of  7 mph.  What bearing should be chosen so that the boat will land at a point exactly across from its starting point?  Give your answer to the nearest tenth of a degree.
a.
8.5°
c.
10.6°
b.
7.1°
d.
79.4°
 

 33. 
Suppose you would like to cross a  205-foot wide river in a boat.  Assume that the boat can travel  33 mph relative to the water and that the current is flowing west at the rate of  5 mph.  If the bearing is chosen so that the boat will land at a point exactly across from its starting point, how long will it take for the boat to make the crossing?  Give your answer to the nearest second.
a.
17 sec
c.
4 sec
b.
2 sec
d.
9 sec
 

 34. 
A box weighing  64 lb is hanging from the end of a rope.  The box is pulled sideways by a horizontal rope with a force of  27 lb.  What angle, to the nearest degree, does the first rope make with the vertical?
a.
46°
c.
12°
b.
23°
d.
35°
 

 35. 
One rope pulls a barge directly east with a force of  42 newtons, and another rope pulls the barge directly north with a force of  68 newtons. Find the magnitude of the resultant force acting on the barge.
a.
2900 newtons
c.
110 newtons
b.
26 newtons
d.
80 newtons
 

 36. 
Two forces, of  53.1 and  25.5 lb, forming an angle of  98.5°, act at a point in the plane. Find the magnitude of the resultant force.
a.
62.2 lb
c.
1300 lb
b.
78.6 lb
d.
55.4 lb
 

 37. 
A hot-air balloon is rising vertically  10 ft/sec while the wind is blowing horizontally at  4 ft/sec.  Find the angle that the balloon makes with the horizontal.
a.
52.8°
c.
21.8°
b.
34.3°
d.
68.2°
 

 38. 
A wind has an easterly component of  9 km/h and a northerly component of  17 km/h.  Find the direction of the wind.
a.
62.1°
c.
27.9°
b.
54.4°
d.
49.5°
 

 39. 
A ship leaves point A and travels directly north to point B. From point B, the ship then travels due east to point C.  The magnitude of the vector from point A to point C is  140.  Find the magnitude of the northern vector.  Find the magnitude of the eastern vector.
a.
70mc039-1.jpg north;  70mc039-2.jpg east
c.
70mc039-4.jpg north; 70 east
b.
70 north;  70mc039-3.jpg east
d.
70 north;  70 east
 

 40. 
What is the minimum force required to prevent a ball weighing  29.8 lb from rolling down a ramp inclined  32.6° with the horizontal?
a.
8.1 lb
c.
25.1 lb
b.
16.1 lb
d.
12.6 lb
 

 41. 
Two boats are pulling a disabled vessel toward the landing dock with forces of  920 lb and  840 lb.  The angle between the forces is  23.7°.  Find the direction and magnitude of the equilibrant.
a.
1723 lb at an angle of  168.7° with the  920-lb force
b.
1723 lb at an angle of  78.7° with the  840-lb force
c.
1723 lb at an angle of  11.3° with the  920-lb force
d.
172 lb at an angle of  168.7° with the  920-lb force
 

 42. 
A force of  38 lb is required to hold a  66 lb toolbox on an incline. What angle does the incline make with the horizontal?
a.
16.7°
c.
73.3°
b.
54.8°
d.
35.2°
 

 43. 
A fishing boat leaves port on a bearing of  30° and travels  13.4 mi. The boat then turns due east and travels mc043-1.jpg  How far is the fishing boat from port, and what is its bearing from port?
a.
15.8 mi;  12.7°
c.
10.1 mi;  12.7°
b.
15.8 mi;  42.7°
d.
11.9 mi;  42.7°
 



 
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