Question 1

The angle between vectors   and   is 30º, and their sum is   . Which vector diagram correctly describes the vectors   ,   and   ?

Accepted Answer

A)  1) 
B)  2) 
C)  3) 
D)  4) 
E)  5) 
A)  1) 
B)  2) 
C)  3) 
D)  4) 
E)  5)

Question 2

You shoot an arrow in a high arc toward a target located some distance away. At the highest point in its flight, the arrow's

Accepted Answer

A)  velocity and acceleration are both nonzero. 
B)  velocity is zero but its acceleration is nonzero. 
C)  velocity is nonzero but its acceleration is zero. 
D)  velocity and acceleration are both zero. 
E)  Insufficient information is given to answer correctly. 
A)  velocity and acceleration are both nonzero. 
B)  velocity is zero but its acceleration is nonzero. 
C)  velocity is nonzero but its acceleration is zero. 
D)  velocity and acceleration are both zero. 
E)  Insufficient information is given to answer correctly.

Question 3

The components of a vector   are Ax = -10 units and Ay = -6 units. What angle does this vector make with the positive x axis?

Accepted Answer

A)  31º 
B)  -31º 
C)  180º - 31º 
D)  180º + 31º 
E)  90º - 31º 
A)  31º 
B)  -31º 
C)  180º - 31º 
D)  180º + 31º 
E)  90º - 31º

Question 4

What angle does the vector   = +5, -12) make with the positive x-axis?

Accepted Answer

A)  67.4º 
B)  22.6º 
C)  36.9º 
D)  53.1º 
E)  292.6º 
A)  67.4º 
B)  22.6º 
C)  36.9º 
D)  53.1º 
E)  292.6º

Question 5

If air resistance is neglected and the initial speed of a projectile is doubled, its range

Accepted Answer

A)  doubles. 
B)  decreases by one-half. 
C)  increases by a factor of four. 
D)  decreases by a factor of four. 
E)  does not change. 
A)  doubles. 
B)  decreases by one-half. 
C)  increases by a factor of four. 
D)  decreases by a factor of four. 
E)  does not change.

Question 6

A projectile is ejected from a 25-m high tower with a velocity of 40 m/s at an angle of 30 degrees to the horizontal first on Earth and then on Mars. What is the ratio of the time taken to hit the ground on Mars compared to Earth? Assume gMars = 0.38gEarth).

Accepted Answer

A)  2.4 
B)  2.6 
C)  0.38 
D)  6.9 
E)  1.0 
A)  2.4 
B)  2.6 
C)  0.38 
D)  6.9 
E)  1.0

Question 7

A car proceeding due south at 60 km/h   ) makes a right turn, after which it is traveling due west at 80 km/h   ).   What is its change in velocity   )?

Accepted Answer

A)  100 km/h 37º north of west 
B)  100 km/h 37º south of west 
C)  20 km/h west 
D)  20 km/h 37º north of west 
E)  20 km/h 37º south of west 
A)  100 km/h 37º north of west 
B)  100 km/h 37º south of west 
C)  20 km/h west 
D)  20 km/h 37º north of west 
E)  20 km/h 37º south of west

Question 8

The vector equation that describes the relationship among vectors   ,   , and   is

Accepted Answer

A)    . 
B)    . 
C)    . 
D)    . 
E)    . 
A)    . 
B)    . 
C)    . 
D)    . 
E)    .

Question 9

The maximum horizontal range of a rock that is thrown at the same speed but different angles with the horizon and that lands at a level, H, below the initial level occurs when the angle is

Accepted Answer

A)  less than 0$\degree$. 
B)  0$\degree$. 
C)  greater than 0$\degree$ and less than 45$\degree$ actual value depends on the value of H). 
D)  45$\degree$, 
E)  greater than 45$\degree$. 
A)  less than 0$\degree$. 
B)  0$\degree$. 
C)  greater than 0$\degree$ and less than 45$\degree$ actual value depends on the value of H). 
D)  45$\degree$, 
E)  greater than 45$\degree$.

Question 10

The position vector of an object is given by   and 4 s later, its position vector is   . The units are in m. The average velocity vector,   in m/s is

Accepted Answer

A)    . 
B)    . 
C)    . 
D)    . 
E)  None of these is correct. 
A)    . 
B)    . 
C)    . 
D)    . 
E)  None of these is correct.

Question 11

You walk 5 km north and then 12 km east. Your resultant displacement is

Accepted Answer

A)  13 km at an angle of 22.6º north of east. 
B)  13 km at an angle of 67.4º north of east. 
C)  17 km at an angle of 22.6º north of east. 
D)  17 km at an angle of 67.4º north of east. 
E)  None of these is correct. 
A)  13 km at an angle of 22.6º north of east. 
B)  13 km at an angle of 67.4º north of east. 
C)  17 km at an angle of 22.6º north of east. 
D)  17 km at an angle of 67.4º north of east. 
E)  None of these is correct.

Question 12

A roofing tile slides down a roof and falls off the roof edge 10 m above the ground at a speed of 6 m/s. The roof makes an angle of 30 degrees to the horizontal. How far from the exit point on the roof does the tile land?

Accepted Answer

A)  6.00 m 
B)  16.0 m 
C)  11.7 m 
D)  13.6 m 
E)  19.2 m 
A)  6.00 m 
B)  16.0 m 
C)  11.7 m 
D)  13.6 m 
E)  19.2 m

Question 13

Two vector quantities, whose directions can be altered at will, can have a resultant of any magnitude between the limits 0 and 200. The magnitude of each vector quantity must therefore be

Accepted Answer

A)  between 0 and 80. 
B)  between 120 and 200. 
C)  less than 100. 
D)  exactly 100. 
E)  more than 100. 
A)  between 0 and 80. 
B)  between 120 and 200. 
C)  less than 100. 
D)  exactly 100. 
E)  more than 100.

Question 14

The initial position and velocity of a projectile are given by   and   respectively, and where r is in m and v in m/s. Ignore air resistance. The position in the horizontal direction in m) as a function of time is

Accepted Answer

A)  xt) = 6t. 
B)  xt) = 3 + 6t. 
C)  xt) = 3 + 6t +   gt2. 
D)  xt) = 4 + 8t. 
E)  xt) = 4 + 8t +   gt2. 
A)  xt) = 6t. 
B)  xt) = 3 + 6t. 
C)  xt) = 3 + 6t +   gt2. 
D)  xt) = 4 + 8t. 
E)  xt) = 4 + 8t +   gt2.

Question 15

A vector A is shown below. The x and y components of the vector are, respectively,

Accepted Answer

A)  A sin $\alpha$, A cos $\alpha$) or A sin $\theta$, A cos$\theta$). 
B)  A sin $\alpha$, A cos $\alpha$) or A cos $\theta$, A sin $\theta$). 
C)  A sin $\alpha$, A sin $\alpha$) or A sin $\theta$, A cos $\theta$). 
D)  A cos $\alpha$, A cos $\alpha$) or A sin$\theta$, A cos $\theta$). 
E)  A cos $\alpha$, A cos $\alpha$) or A cos $\theta$, A cos $\theta$). 
A)  A sin $\alpha$, A cos $\alpha$) or A sin $\theta$, A cos$\theta$). 
B)  A sin $\alpha$, A cos $\alpha$) or A cos $\theta$, A sin $\theta$). 
C)  A sin $\alpha$, A sin $\alpha$) or A sin $\theta$, A cos $\theta$). 
D)  A cos $\alpha$, A cos $\alpha$) or A sin$\theta$, A cos $\theta$). 
E)  A cos $\alpha$, A cos $\alpha$) or A cos $\theta$, A cos $\theta$).

Question 16

You walk 12 km south and then 5 km east. Your resultant displacement is

Accepted Answer

A)  13 km at an angle of 22.6º south of east. 
B)  13 km at an angle of 67.4º south of east. 
C)  17 km at an angle of 22.6º south of east. 
D)  17 km at an angle of 67.4º south of east. 
E)  None of these is correct. 
A)  13 km at an angle of 22.6º south of east. 
B)  13 km at an angle of 67.4º south of east. 
C)  17 km at an angle of 22.6º south of east. 
D)  17 km at an angle of 67.4º south of east. 
E)  None of these is correct.

Question 17

The curve shows the position of an object with time. The object moves with a constant speed, v.   Which of the vector diagrams below best represent the change in position vector from P1 to P2?

Accepted Answer

A)  1) 
B)  2) 
C)  3) 
D)  4) 
E)  None of these is correct. 
A)  1) 
B)  2) 
C)  3) 
D)  4) 
E)  None of these is correct.

Question 18

A projectile is shot at an angle of 45º to the horizontal near the surface of Earth but in the absence of air resistance. When it reaches the highest point of its trajectory, its speed is 150 m/s. In a second trial with the same projectile, the initial speed is the same but the angle is now 37º with the horizontal. At its highest point in this trajectory, the speed of the projectile would be

Accepted Answer

A)  150 m/s sin 45º/sin 36º). 
B)  150 m/s cos 37º/cos 45º). 
C)  150 m/s sin 37º/sin 45º). 
D)  150 m/s (37/45). 
E)  None of these is correct. 
A)  150 m/s sin 45º/sin 36º). 
B)  150 m/s cos 37º/cos 45º). 
C)  150 m/s sin 37º/sin 45º). 
D)  150 m/s (37/45). 
E)  None of these is correct.

Question 19

Which of the following vector equations correctly describes the relationship among the vectors shown in the figure below?

Accepted Answer

A)    
B)    
C)    
D)    
E)  None of these equations are correct. 
A)    
B)    
C)    
D)    
E)  None of these equations are correct.

Question 20

The position vector of an object is given by   and 4 s later, its position vector is   . The units are in m. The change in the position vector   , in m, is

Accepted Answer

A)    . 
B)    . 
C)    . 
D)    . 
E)  None of these is correct. 
A)    . 
B)    . 
C)    . 
D)    . 
E)  None of these is correct.

Exam 3: Motion in Two and Three Dimensions

The angle between vectors and is 30º, and their sum is . Which vector diagram correctly describes the vectors , and ?

You shoot an arrow in a high arc toward a target located some distance away. At the highest point in its flight, the arrow's

The components of a vector are Ax = -10 units and Ay = -6 units. What angle does this vector make with the positive x axis?

What angle does the vector = +5, -12) make with the positive x-axis?

If air resistance is neglected and the initial speed of a projectile is doubled, its range

A projectile is ejected from a 25-m high tower with a velocity of 40 m/s at an angle of 30 degrees to the horizontal first on Earth and then on Mars. What is the ratio of the time taken to hit the ground on Mars compared to Earth? Assume gMars = 0.38gEarth).

A car proceeding due south at 60 km/h ) makes a right turn, after which it is traveling due west at 80 km/h ). What is its change in velocity )?

The vector equation that describes the relationship among vectors , , and is

The maximum horizontal range of a rock that is thrown at the same speed but different angles with the horizon and that lands at a level, H, below the initial level occurs when the angle is

The position vector of an object is given by and 4 s later, its position vector is . The units are in m. The average velocity vector, in m/s is

You walk 5 km north and then 12 km east. Your resultant displacement is

A roofing tile slides down a roof and falls off the roof edge 10 m above the ground at a speed of 6 m/s. The roof makes an angle of 30 degrees to the horizontal. How far from the exit point on the roof does the tile land?

Two vector quantities, whose directions can be altered at will, can have a resultant of any magnitude between the limits 0 and 200. The magnitude of each vector quantity must therefore be

The initial position and velocity of a projectile are given by and respectively, and where r is in m and v in m/s. Ignore air resistance. The position in the horizontal direction in m) as a function of time is

A vector A is shown below. The x and y components of the vector are, respectively,

You walk 12 km south and then 5 km east. Your resultant displacement is

The curve shows the position of an object with time. The object moves with a constant speed, v. Which of the vector diagrams below best represent the change in position vector from P1 to P2?

Which of the following vector equations correctly describes the relationship among the vectors shown in the figure below?

The position vector of an object is given by and 4 s later, its position vector is . The units are in m. The change in the position vector , in m, is

Introduction to Physics

Linear Motion

Forces and Motion I: Newtons Laws

Forces and Motion II: Applications

Work and Energy

Momentum, Collisions, and the Center of Mass

Rotational Motion

Elastic Properties of Matter: Stress and Strain

Gravitation

Fluids

Oscillations

Waves

Thermodynamics I

Thermodynamics II

Electrostatics I: Electric Charge, Forces, and Fields

Electrostatics II: Electric Potential Energy and Electric Potential

Electric Charges in Motion

Magnetism

Electromagnetic Induction

Alternating-Current Circuits

Electromagnetic Waves

Wave Properties of Light

Geometrical Optics

Relativity

Quantum Physics and Atomic Structure

Nuclear Physics

Particle Physics

Filters

The components of a vector are A_x = -10 units and A_y = -6 units. What angle does this vector make with the positive x axis?

A projectile is ejected from a 25-m high tower with a velocity of 40 m/s at an angle of 30 degrees to the horizontal first on Earth and then on Mars. What is the ratio of the time taken to hit the ground on Mars compared to Earth? Assume g_Mars = 0.38g_Earth).

The curve shows the position of an object with time. The object moves with a constant speed, v. Which of the vector diagrams below best represent the change in position vector from P₁ to P₂?