[ Questions #19  Questions #1045  Questions #4655  Questions #5672 ] 
1. Which of the following statements are true of scalars and vectors? List all that are TRUE.
2. Which of the following quantities are vectors? Include all that apply.
3. Numerical values and directions are stated for a variety of quantities. Which of these statements represent a vector description? Include all that apply.
4. Which of the following statements are true of vector addition, vector subtraction, and vector addition diagrams? List all that apply.
5. Which of the following descriptions of moving objects accurately portray a projectile? List all that apply.
6. Which of the following statements are true of projectiles? List all that apply.
7. Which of the following statements are true of the horizontal motion of projectiles? List all that apply.
8. Which of the following statements are true of the vertical motion of projectiles? List all that apply.
9. Which of the following statements are true of the time of flight for a projectile? List all that apply.
10. If two displacement vectors of 6 meters and 8 meters (with varying directions) are added together, then the resultant could range anywhere between ___ meters and ___ meters.
a. 0, 48 
b. 1.33, 48 
c. 0, 14 
d. 2, 14 
e. ... nonsense! No such prediction can be made. 

f. ... nonsense! A prediction can be made but none of these choices are correct. 
11. Three vectors are added following the rules of vector addition. A fourth vector is drawn from the tail of the first vector to the head of the last vector. This fourth vector is referred to as ____.
a. the equilibrant b. the hypotenuse c. the resultant d. a mistake
The order in which vectors is added will effect the end result.
a. True b. False
13. Vector A is directed northward and vector B is directed eastward. Which of the following vector addition diagrams best represent the addition of vectors A and B and the subsequent resultant?
14. When adding vector B to vector A geometrically (or graphically) using the head to tail method, the resultant is drawn from ____ to the ____.
a. head of A, tail of B b. tail of A, head of B c. head of B, tail of A d. tail of B, head of A
Use the following vector addition diagrams for questions #15#20.
15. Which one of the following vector addition equations is shown in Diagram 1?
a. A + B = C b. A + C = B c. B + C = A d. B + A = C e. C + B = A f. C + A = B g. None of these
16. Which one of the following vector addition equations is shown in Diagram 2?
a. A + B = C b. A + C = B c. B + C = A d. B + A = C e. C + B = A f. C + A = B g. None of these
17. Which one of the following vector addition equations is shown in Diagram 3?
a. A + B = C b. A + C = B c. B + C = A d. B + A = C e. C + B = A f. C + A = B g. None of these
18. Which one of the following vector addition equations is shown in Diagram 4?
a. A + B = C b. A + C = B c. B + C = A d. B + A = C e. C + B = A f. C + A = B g. None of these
19. Consider the magnitude and direction of vectors A and B as shown in Diagram 1 above. Which one of the following diagrams would represent B  A = R?
20. Consider the magnitude and direction of vectors B and C as shown in Diagram 2 above. Which one of the following diagrams would represent C  B = R?
21. The vector sum (magnitude only) of 25.0 m, north + 18.0 m, East is ___ m.
a. 7.00 b. 21.5 c. 30.8 d. 35.8 e. 43.0 f. 54.2 g. 949 h. None of these
22. The vector sum (magnitude only) of 32.0 m, north + 41.0 m, west is ___ m.
a. 9.00 b. 36.5 c. 38.0 d. 52.0 e. 73.0 f. 128 g. 2705 h. None of these
Use the diagram below to answer questions #23#28. Each square on the diagram represents a 20meter x 20meter area.
23. If a person walks from D to H to G to C, then the distance walked is ____ meters.
a. 128 b. 180 c. 401 d. 460 e. 480 f. 533 g. 620 h. None of these
24. If a person walks from D to H to G to C, then the magnitude of the displacement is ____ meters.
a. 128 b. 180 c. 401 d. 460 e. 480 f. 533 g. 620 h. None of these
25. If a person walks from D to H to G to C, then the direction of the displacement is ___ degrees (as measured counterclockwise from East).
a. 38.7 b. 51.3 c. 53.1 d. 216.9 e. 218.7 f. 231.3 g. 233.1 h. None of these
26. If a person walks from H to E to C to G, then the distance walked is ____ meters.
a. 80.0 b. 240. c. 253 d. 333 e. 493 f. 560. g. 640. h. None of these
27. If a person walks from H to E to C to G, then the magnitude of the displacement is ____ meters.
a. 80.0 b. 240. c. 253 d. 333 e. 493 f. 560. g. 640. h. None of these
28. If a person walks from H to E to C to G, then the direction of the displacement is ___ degrees (as measured counterclockwise from East).
a. 0 b. 18.4 c. 71.6 d. 90.0 e. 108.4 f. 161.6 g. 341.6 h. None of these
Use the following diagram for questions #29#33. In the diagram, a riverboat is shown starting at position A on the east bank of a river. The boat heads towards position B (a point directly across the river from A) with a speed of 3.8 m/s. But because of a current with a speed of 1.8 m/s, the boat lands on the west bank of the river at position C, a location downstream from B. The width of the river (d_{across}) is 86.4 meters.
29. The magnitude of the resultant velocity of the boat is ____ m/s.
a. 1.8 b. 2.0 c. 3.35 d. 3.80 e. 4.20 f. 5.60 g.11.2 h. None of these
30. The direction of the resultant velocity of the boat is ____ m/s.
a. 0 b. 18.4 c. 71.6 d. 90.0 e. 108.4 f. 161.6 g. 341.6 h. None of these
31. The time required for the boat to cross the 86.4 m wide river is ___ seconds.
a. 4.20 b. 15.4 c. 20.5 d. 22.7 e. 48.0 f. None of these
32. Location C is the location where the boat ultimately lands on the opposite shore. What is the distance from location B to location C.
a. 37.0 b. 40.9 c. 78.1 d. 86.4 e. 95.6 f. 182 g. 202 h. None of these
33. If the current on a particular day was flowing with two times the velocity, then the time to cross the river would be ____.
a. two times greater b. onehalf as great c. greater, but not two times greater d. less, but not onehalf the original time e. the same as it was when the current flowed at 1.8
m/s.
34. An object is undergoing free fall motion. As it falls, the object's ____.
a. speed increases 
b. acceleration increases 
c. both of these 
d. none of these 
35. A football is kicked into the air at an angle of 45 degrees with the horizontal. At the very top of the ball's path, its velocity is _______.
a. entirely vertical 
b. entirely horizontal 
c. both vertical and horizontal 
d. not enough information given to know. 
36. A football is kicked into the air at an angle of 45 degrees with the horizontal. At the very top of the ball's path, its acceleration is _______. (Neglect the effects of air resistance.)
a. entirely vertical 
b. entirely horizontal 
c. both vertical and horizontal 
d. not enough information given to know. 
37. A football is kicked into the air at an angle of 45 degrees with the horizontal. At the very top of the ball's path, the net force acting upon it is _______. (Neglect the effects of air resistance.)
a. entirely vertical 
b. entirely horizontal 
c. both vertical and horizontal 
d. not enough information given to know. 
38. At what point in its path is the horizontal component of the velocity (v_{x}) of a projectile the smallest?
a. The instant it is thrown. 
b. Halfway to the top. 
c. At the top. 
d. As it nears the top. 
e. It is the same throughout the path. 
39. At what point in its path is the vertical component of the velocity (v_{y}) of a projectile the smallest?
a. The instant it is thrown. 
b. Halfway to the top. 
c. At the top. 
d. As it nears the top. 
e. It is the same throughout the path. 
40. An airplane that flies at 100 km/h in a 100 km/h hurricane crosswind has a speed (relative to the ground) of ____.
a. 0 km/h 
b. 100 km/h 
c. 141 km/h 
d. 200 km/h 
41. An airplane moves at 141 km/h toward the northeast (45 degrees). What is its component velocity in the northward direction?
a. 41 km/h 
b. 100 km/h 
c. 110 km/h 
d. 141 km/h 
42. Roll a bowling ball off the edge of a table. As it falls, its horizontal component of velocity ___.
a. decreases 
b. remains constant 
c. increases 
43. A bullet is fired horizontally and hits the ground in 0.5 seconds. If it had been fired with twice the speed in the same direction, it would have hit the ground in ____. (Assume no air resistance)
a. less than 0.5 s. 
b. more than 0.5 s. 
c. 0.5 s. 
44. A projectile is launched at an angle of 15 degrees above the horizontal and lands down range. For the same speed, what other projection angle would produce the same downrange distance?
a. 30 degrees. 
b. 45 degrees. 
c. 50 degrees. 
d. 75 degrees 
e. 90 degrees. 
45. Two projectiles are fired at equal speeds but different angles. One is fired at angle of 30 degrees and the other at 60 degrees. The projectile to hit the ground first will be the one fired at (neglect air resistance) ____.
a. 30 degrees 
b. 60 degrees 
c. both hit at the same time 
46. Express the direction of each of the following vectors in the diagram below.






47. In the following diagrams, two vectors are being added and the resultant is drawn. For each diagram, identify which vector is the resultant and write the equation (e.g., A + B = C).
The resultant is vector _____. The equation is ____ + ____ = _____ 
The resultant is vector _____. The equation is ____ + ____ = _____ 
The resultant is vector _____. The equation is ____ + ____ = _____ 
The resultant is vector _____. The equation is ____ + ____ = _____ 
48. Consider the five vectors shown below; they are labeled A, B, C, D and E.
Use the stated magnitude and direction of these vectors to sketch a vector addition diagram for the following vector operations and determine the resultant. You only need to construct an approximate sketch; there is no need to do a scaled diagram.
49. A hiker's motion can be described by the following three displacement vectors.
Add the three displacement vectors using the headtotail method of vector addition. Then answer the following two questions.
(a) What is the distance walked by the hiker?(b) What is the resulting displacement of the hiker?
50. Solve the following problem using a vector addition diagram.
A hiker hikes for 12 km, west. She then makes a turn and hikes in a straight line until she reaches her final destination. If the resultant displacement is 21 km at 147 degrees, then what was the displacement (magnitude and direction) of the second leg of the hike?
51. Consider the trajectory diagram shown below for a horizontally launched projectile. On the diagram, draw vector arrows representing the v_{x} and v_{y} velocity components during the course of the motion. The length of the arrows should represent the magnitude of the velocity components. Label each component. (Note that the velocity components are already shown for the first position.)
52. Consider the trajectory diagram shown below for a nonhorizontally launched projectile. On the diagram, draw vector arrows representing the v_{x} and v_{y} velocity components during the course of the motion. The length of the arrows should represent the magnitude of the velocity components. Label each component. (Note that the velocity components are already shown for the first position.)
53. Consider the diagram below. The blue path represents the trajectory of a projectile dropped from rest from the top of the path. (Each ball location represents the location after a 1second interval of time.) The red path represents the trajectory of the same ball thrown horizontally in the absence of gravity. Construct a third path accurately showing the trajectory of a projectile launched with the same horizontal speed as the red ball. Show the location during the first four seconds of motion. Finally, the (x, y) coordinate position of location 1 is (0 m, 5 m) and the (x, y) coordinate position of location 2 is (15 m, 0 m). Determine the (x, y) coordinate positions of the four locations in your trajectory. (Assume g ~10 m/s/s.)
54. Consider the map of the United States at the right. Given the scale that 1 cm = 500 km, use a protractor and a ruler to determine the displacement of a traveler for the listed trips. A couple trips include two "legs." Indicate both the magnitude and the direction (using the counterclockwise from East convention) for the resultant displacement vector of the traveler.
Trip 


a. From Chicago (CHI) to Washington, DC (WSH) 

b. From Chicago (CHI) to Seattle (SEA) 

c. From Jackson Hole (JXH) to Houston (HST) 

d. From Denver (DEN) to Phoenix (PHX) to Washington (WSH) 

e. From Salt Lake City (SLC) to Reno (REN) to Miami (MIA) 
55. A cannonball is launched from the top of a 125meter high cliff with an initial horizontal speed of 20 m/s. The (x, y) coordinate position of the launch location is designated as the (0, 0) position. Determine the (x, y) coordinate positions of the cannonball at 1second intervals during its path to the ground. Assume g~10 m/s/s.
56. In the Vector Addition Lab, Anna starts at the classroom door and walks:
Using either a scaled diagram or a calculator, determine the magnitude and direction of Anna's resulting displacement.
57. In a grocery store, a shopper walks 36.7 feet down an aisle. She then turns left and walks 17 feet straight ahead. Finally, she turns right and walks 8.2 feet to a final destination. (a) Determine the magnitude of the overall displacement. (b) Determine the direction of the displacement vector relative to the original line of motion.
58. A hiker hikes 12.4 km, south. The hiker then makes a turn towards the southeast and finishes at the final destination. The overall displacement of the twolegged trip is 19.7 km at 309 degrees . Determine the magnitude and direction of the second leg of the trip.
59. A boat heads straight across a river which is 100 meters wide. For the following two combinations of boat velocities and current velocities, determine the resultant velocity, the time required to cross the river, and the distance traveled downstream.
Given: Boat velocity = 10 m/s, East River velocity = 4 m/s, North Calculate: Resultant Vel. (mag. & dir'n): ________ Time to cross river: _________ Distance traveled downstream: _______ 
Given: Boat velocity = 8 m/s, East River velocity = 5 m/s, South Calculate: Resultant Vel. (mag. & dir'n): ________ Time to cross river: _________ Distance traveled downstream: _______ 
60. The diagram at the right depicts a horizontallylaunched projectile leaving a cliff of height y with a horizontal velocity (v_{ix}) and landing a distance x from the base of the cliff. Express your understanding of projectile kinematics by filling in the blanks in the table below. To simplify the calculations, use an acceleration of gravity value of 10 m/s/s.


61. The launch velocity and angle is given for three different projectiles. Use trigonometric functions to resolve the velocity vectors into horizontal and vertical velocity components. Then use kinematic equations to determine the time that the projectile is in the air, the height to which it travels (when it is at its peak), and the horizontal distance that it travels. (To simplify the calculations, use an acceleration of gravity value of 10 m/s/s.)
Given: Launch Vel. = 30 m/s Launch angle = 30 degrees 
Given: Launch Vel. = 30 m/s Launch angle = 45 degrees 
Given: Launch Vel. = 30 m/s Launch angle = 50 degrees 
v_{ix} = __________ v_{iy} = ___________ t_{up} = ___________ t_{total} = ___________ y at peak = ___________ x = ___________ 
v_{ix} = __________ v_{iy} = ___________ t_{up} = ___________ t_{total} = ___________ y at peak = ___________ x = ___________ 
v_{ix} = __________ v_{iy} = ___________ t_{up} = ___________ t_{total} = ___________ y at peak = ___________ x = ___________ 
62. If a projectile is launched horizontally with a speed of 12.0 m/s from the top of a 24.6meter high building. Determine the horizontal displacement of the projectile.
63. A projectile is launched with an initial speed of 21.8 m/s at an angle of 35degrees above the horizontal.
(a) Determine the time of flight of the projectile.(b) Determine the peak height of the projectile.
(c) Determine the horizontal displacement of the projectile.
64. A projectile is launched horizontally from the top of a 45.2meter high cliff and lands a distance of 17.6 meters from the base of the cliff. Determine the magnitude of the launch velocity.
65. Two Glenview students stand on the top of their 3.29meter secondstory deck and launch a water balloon from a homemade winger. The balloon is launched upward at a speed of 45.2 m/s and an angle of 39.1 degrees. The balloon lands in a retention pond whose surface is 2.92 meters below grade. Determine the horizontal distance from launch location to landing location.
66. A place kicker kicks a football from 39.6 meters from the goal posts. The kick leaves the ground with a speed of 24.8 m/s at an angle of 49.6 degrees. The goal posts are 3.10meters high.
(a) Determine the amount by which the kick clears the goal posts.(b) For this given launch velocity, what is the longest field goal (in yards) which could have been kicked? Assume that the football hits the horizontal crossbar of the posts and bounces through. Given: 1 meter = 3.28 feet.
67. An airplane starts at Point A and flies 210 km at 311 degrees to Point B. The plane then flies 179 km at 109 degrees to Point C. Finally, the plane flies 228 km at 29 degrees to Point D. Determine the resulting displacement (magnitude and direction) from Points A to D.
68. Sammy Sosa clubs a homerun which sails 421 feet and lands on an apartment balcony located a vertical distance of 59 feet above the level of the ballbat contact location. An observer times the flight to the balcony to take 3.4 seconds.
(a) Determine the velocity (magnitude and angle) at which the ball leaves the bat.(b) Determine the speed of the ball (in miles/hour) when it lands in the bleachers.
Given: 1 m/s = 2.24 mi/hr; 1 meter = 3.28 feet.
69. An unfortunate accident occurred on the toll way. A driver accidentally passed through a faulty barricade on a bridge (quite unfortunately). and landed in a pile of hay (quite fortunately). Measurements at the accident scene reveal that the driver plunged a vertical distance of 8.26 meters. The car carried a horizontal distance of 42.1 meters from the location where it left the bridge. If the driver was in a 65 mi/hr speed zone, then determine the amount by which the driver was exceeding the speed limit at the time of the accident. Assume that the contact with the barricade did not slow the car down. (1 m/s = 2.24 mi/hr)
70. Cupid wishes to shoot an arrow through the open window of a tall building. The window is 32.8 meters above the ground and Cupid stands 63.6 meters from the base of the building. If Cupid aims the arrow at an angle of 51.5 degrees above the horizontal, with what minimum speed must he fire the arrow in order for it to enter the window?
71. In a Physics demonstration, a projectile is launched from a height of 1.23 m above the ground with a speed of 10.6 m/s at an angle of 30 degrees above the horizontal.
(a) What horizontal distance from the launch location will the projectile land?(b) With what speed does the projectile land?
72. A car is parked on a cliff overlooking the sea. The cliff is inclined at an angle of 29 degrees below the horizontal. The negligent driver leaves the car in neutral and it begins rolling from rest towards the cliff's edge with an acceleration 4.5 m/s/s. The car moves a linear distance of 57.2 m to the edge of the cliff before plunging into the ocean below. The cliff is 42.2 m above the sea.
(a) Find the speed (in m/s) of the car the moment it leaves the cliff.(b) Find the time (in seconds) it takes the car to drop to the water below the edge of the cliff.
(c) Find the position (in meters) of the car relative to the base of the cliff when it lands in the sea.
[ Questions #19  Questions #1045  Questions #4655  Questions #5672 ] 
Last update: 4/30/02