Motion in TwoDimensions
1. If an object has an acceleration of 0 m/s^{2}, then one can be sure that the object is not
a. moving 
b. changing position 
c. changing velocity 

Acceleration (14 seconds) 
2. Which one of the following is NOT consistent with a car which is accelerating?

Acceleration (14 seconds) 
3. Barry Sanders is running down the football field in a straight line. He starts at the 0yard line at 0 seconds. At 1 second, he is on the 10yard line; at 2 seconds, he is on the 20yard line; at 3 seconds, he is on the 30yard line; and at 4 seconds, he is on the 40yard line. This is evidence that

Acceleration (14 seconds)  Speed vs. Velocity (8 seconds) 
4. Barry Sanders is running down the football field in a straight line. He starts at the 0yard line at 0 seconds. At 1 second, he is on the 10yard line; at 2 seconds, he is on the 20yard line; at 3 seconds, he is on the 30yard line; and at 4 seconds, he is on the 40yard line. What is Barry's acceleration?

Acceleration (14 seconds)  Speed vs. Velocity (8 seconds) 
5. If an object is moving eastward and slowing down, then the direction of its acceleration vector is
a. eastward 
b. westward 
c. neither 
d. not enough info to tell 

Acceleration (14 seconds) 
6. Which one of the following quantities is NOT a vector?
a. 10 mi/hr, east 
b. 10 mi/hr/sec, west 
c. 35 m/s, north 
d. 20 m/s 

Scalars vs. Vectors (3 seconds) 
7. Which one of the following statements is NOT true of a freefalling object? An object in a state of free fall
a. falls with a constant speed of 10 m/s. 
b. falls with a acceleration of 10 m/s/s. 
c. falls under the sole influence of gravity. 
d. falls with an acceleration of constant magnitude. 

Introduction to Free Fall (4 seconds)  The Acceleration of Gravity (6 seconds) 
8. What is the acceleration of a car that maintains a constant velocity of 100 km/hr for 10 seconds?
a. 0 
b. 10 km/hr/s 
c. 10 km/s/s 
d. 1000 km/hr/s 

Acceleration (14 seconds) 
9. As an object freely falls, its
a. speed increases 
b. acceleration increases 
c. both of these 
d. none of these 

Introduction to Free Fall (4 seconds)  The Acceleration of Gravity (6 seconds) 
10. A ball is thrown into the air at some angle between 0 and 90 degrees. 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. 

Projectiles: Horizontal and Vertical Components of Velocity (11 seconds)  Projectile Animation (15 seconds) 
11. A ball is thrown into the air at some angle between 0 and 90 degrees. At the very top of the ball's path, its acceleration is _______.
a. entirely vertical 
b. entirely horizontal 
c. both vertical and horizontal 
d. not enough information given to know. 

Characteristics of a Projectile's Trajectory (12 seconds) 
12. A ball is thrown into the air at some angle between 0 and 90 degrees. Neglecting air resistance, at the very top of the ball's path, the net force acting upon it is _______.
a. entirely vertical 
b. entirely horizontal 
c. both vertical and horizontal 
d. not enough information given to know. 

Characteristics of a Projectile's Trajectory (12 seconds) 
13. At what point in its path is the horizontal component of the velocity of a projectile the smallest?
a. when 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. 


Projectiles: Horizontal and Vertical Components of Velocity (11 seconds)  Projectile Animation (12 seconds) 
14. At what point in its path is the vertical component of the velocity of a projectile the smallest?
a. when it is thrown. 
b. halfway to the top. 
c. at the top. 
d. as it nears the ground. 
e. it is the same throughout the path. 


Projectiles: Horizontal and Vertical Components of Velocity (11 seconds)  Projectile Animation (15 seconds) 
15. An airplane that flies at 100 km/h in a 100 km/h hurricane crosswind has a ground speed of
a. 0 km/h 
b. 100 km/h 
c. 141 km/h 
d. 200 km/h 

Relative Velocity and Riverboat Problems  The Plane and The Wind Animation (9 seconds) 
16. An airplane travels at 141 km/h toward the northeast (45 degrees). What is its component velocity due north?
a. 41 km/h 
b. 100 km/h 
c. 110 km/h 
d. 141 km/h 

Vector Components (15 seconds) 
17. 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 

Projectiles: Horizontal and Vertical Components of Velocity (11 seconds)  Projectile Animation (12 seconds) 
18. A bullet fired horizontally 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. 

Horizontal and Vertical Components of Displacement (13 seconds) 
19. A projectile is launched at an angle of 15 degrees above the horizontal and lands down range. What other projection angle for the same speed would produce the same downrange distance?
a. 30 degrees. 
b. 45 degrees. 
c. 50 degrees. 
d. 75 degrees 
e. 90 degrees. 
20. 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 

Maximum Range Animation (13 seconds) 
21. Express the direction of each of the following vectors in the diagram below.
A: ______ 
B: ______ 
C: ______ 
D: ______ 
E: ______ 
F: ______ 

Vectors and Direction (11 seconds) 
22. 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).
a. The resultant is vector _____. The equation is ____ + ____ = _____ 
b. The resultant is vector _____. The equation is ____ + ____ = _____ 
c. The resultant is vector _____. The equation is ____ + ____ = _____ 
d. The resultant is vector _____. The equation is ____ + ____ = _____ 

Vector Addition (20 seconds)  Resultants (6 seconds) 
23. A hiker's motion can be described by the following three displacement vectors.
22 km, 45 degrees + 16 km, 135 degrees + 12 km, 270 degrees
Add the three displacement vectors using the headtotail method of vector addition. Then answer the following two questions.

Vector Addition (20 seconds)  Resultants (6 seconds)  Distance vs. Displacement (7 seconds) 
Consider the following statements in answering the next three questions.
24. If an object is known to be at equilibrium, then which of the following statements MUST be true?
25. If an object is known to be at equilibrium, then which of the following statements MUST NOT be true?
26. If an object is known to be at equilibrium, then which of the following statements COULD be true?

Equilibrium and Statics (23 seconds)  Acceleration (14 seconds) 
27. What is the maximum resultant force resulting from a 3N force and an 8N force? ______
28. What is the minimum resultant force resulting from a 3N force and an 8N force? ______

Vector Addition (20 seconds)  Addition of Forces (19 seconds) 
29. 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.
a. 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: _______ 
b. 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: _______ 

Relative Velocity and Riverboat Problems (10 seconds) 
30. 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.



Horizontally Launched Projectiles  ProblemSolving (10 seconds) 
31. 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.
a. Given: Launch Vel. = 30 m/s Launch angle = 30 degrees 
b. Given: Launch Vel. = 30 m/s Launch angle = 45 degrees 
c. Given: Launch Vel. = 30 m/s Launch angle = 50 degrees 
Calculate: v_{ix} = __________ v_{iy} = ___________ t_{up} = ___________ t_{total} = ___________ y at peak = ___________ x = ___________ 
Calculate: v_{ix} = __________ v_{iy} = ___________ t_{up} = ___________ t_{total} = ___________ y at peak = ___________ x = ___________ 
Calculate: v_{ix} = __________ v_{iy} = ___________ t_{up} = ___________ t_{total} = ___________ y at peak = ___________ x = ___________ 

NonHorizontally Launched Projectiles  ProblemSolving (7 seconds) 
32. What angle above gives the projectile the maximum range (i.e., maximum horizontal displacement)?

Maximum Range Animation (13 seconds) 
33. 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.

Horizontally Launched Projectiles  ProblemSolving (10 seconds) 
34. A projectile is launched with an initial speed of 21.8 m/s at an angle of 35degrees above the horizontal. Determine the horizontal displacement of the projectile.

NonHorizontally Launched Projectiles  ProblemSolving (7 seconds) 
35. The signs in the two diagrams below hang at equilibrium by means of two cables which are arranged symmetrically. The tension in both cables and the angle between the cables is indicated. Use trigonometric functions and force principles to determine the mass and the weight of the following three signs.
a.

b.

mass = __________ Weight = _________ 
mass = __________ Weight = _________ 

Resolution of Forces (22 seconds)  Equilibrium and Statics (23 seconds) 
36. The signs in the two diagrams below hang at equilibrium by means of two cables which are arranged symmetrically. The mass of the sign and the angle between the cables is indicated. Use trigonometric functions and force principles to determine the tension in the cables.
a. m = 5 kg 
b. m = 8 kg 
Tension = __________ 
Tension = __________ 

Resolution of Forces (22 seconds)  Equilibrium and Statics (23 seconds) 
37. The following diagrams depict a force being applied at an angle in order to accelerate an object across a rough surface. For each case, determine the values of all missing quantities (F_{grav}, F_{norm}, F_{frict}, F_{net}, and acceleration).
a. m = 12 kg F_{net} = __________, ________ (dir'n) a = __________, ________ (dir'n) 
b. m = 8 kg F_{net} = __________, ________ (dir'n) a = __________, ________ (dir'n) 

Net Force Problems Revisited (17 seconds) 
38. The following diagrams depict an object of known mass upon an incline with a known coefficient of friction and angle. For each case, determine all missing quantities.
a. m = 12 kg F_{parallel} = _______ F_{perpendicular} = _______ F_{net} = __________, ________ (dir'n) a = __________, ________ (dir'n) 
b. m = 8 kg F_{parallel} = _______ F_{perpendicular} = _______ F_{net} = __________, ________ (dir'n) a = __________, ________ (dir'n)


Inclined Planes (25 seconds) 
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This page last updated on November 11, 1998.