Question 1

A vector   has components Ax = 12 m and Ay = 5.0 m. What is the magnitude of vector   ?

Accepted Answer

A) 7.0 m 
B) 13 m 
C) 17 m 
D) 60 m 
E) 169 m 
A) 7.0 m 
B) 13 m 
C) 17 m 
D) 60 m 
E) 169 m

Question 2

A projectile is fired from ground level with an initial speed of 55.6 m/s at an angle of 41.2° above the horizontal.
(a) Determine the time necessary for the projectile to reach its maximum height.
(b) Determine the maximum height reached by the projectile.
(c) Determine the horizontal and vertical components of the velocity vector at the maximum height.
(d) Determine the horizontal and vertical components of the acceleration vector at the maximum height.

Accepted Answer

(a) 3.73 s
(b) 68.3

Question 3

For general projectile motion, the horizontal component of a projectile's velocity

Accepted Answer

A) is zero. 
B) remains a non-zero constant. 
C) continuously increases. 
D) continuously decreases. 
E) any of the above, depending on position. 
A) is zero. 
B) remains a non-zero constant. 
C) continuously increases. 
D) continuously decreases. 
E) any of the above, depending on position.

Question 4

For a projectile launched horizontally, the vertical component of its velocity

Accepted Answer

A) is zero. 
B) remains a non-zero constant. 
C) continuously increases. 
D) continuously decreases. 
E) any of the above, depending on position. 
A) is zero. 
B) remains a non-zero constant. 
C) continuously increases. 
D) continuously decreases. 
E) any of the above, depending on position.

Question 5

An object has a velocity   0(t) = (3.00 m/s)   + (1.00 m/s)   at time t = 0.00 s. The acceleration of the object is   (t) = (2.00 m/s3)t   + (1.00 m/s4)t2  
  . If the object is located at   0(t) = (1.00 m)   + (-1.00 m)   at time t = 0.00 s., what is the position of the object at time t = 1.00 s?

Accepted Answer

A) ( 2.72 m)   + ( 6.14 m)   
B) ( 4.33 m)   + ( 0.0833 m)   
C) ( 2.00 m)   + ( 1.00 m)   
D) ( 5.32 m)   + ( 1.34 m)   
E) ( 0.333 m)   + ( 0.0833 m)   
A) ( 2.72 m)   + ( 6.14 m)   
B) ( 4.33 m)   + ( 0.0833 m)   
C) ( 2.00 m)   + ( 1.00 m)   
D) ( 5.32 m)   + ( 1.34 m)   
E) ( 0.333 m)   + ( 0.0833 m)

Question 6

A child throws a ball with an initial speed of 8.00 m/s at an angle of 40.0° above the horizontal. The ball leaves her hand 1.00 m above the ground. What is the magnitude of the ball's velocity just before it hits the ground?

Accepted Answer

A) 1.22 m/s 
B) 6.79 m/s 
C) 7.45 m/s 
D) 9.14 m/s 
E) 4.58 m/s 
A) 1.22 m/s 
B) 6.79 m/s 
C) 7.45 m/s 
D) 9.14 m/s 
E) 4.58 m/s

Question 7

Vector   is 75.0 cm long and points at 30° above the positive x axis. Vector   is 25.0 cm long and points along the negative x axis. Vector   is 40.0 cm long and points at 45° below the negative x axis.
(a) Determine the x and y components of Vector   .
(b) Determine the x and y components of Vector   .
(c) Determine the x and y components of Vector   .
(d) Determine the sum of these three vectors in terms of components.
(e) Determine the sum of these three vectors in terms of magnitude and direction.

Accepted Answer

(a) A_x = 65 cm, A_y = 38 cm (b) B

Question 8

Vector   =   -   . Under what condition is    =   +   ?

Accepted Answer

A) Vectors   and
  are in the same direction. 
B) Vectors   and
  are in opposite directions. 
C) The statement is always true. 
D) The statement is never true. 
E) Vectors   and
  are in perpendicular directions. 
A) Vectors   and
  are in the same direction. 
B) Vectors   and
  are in opposite directions. 
C) The statement is always true. 
D) The statement is never true. 
E) Vectors   and
  are in perpendicular directions.

Question 9

Vector   has a magnitude 5.00 and points in a direction 60.0° clockwise from the negative y axis. What are the x and y components of vector   .

Accepted Answer

A) Ax = 2.50 and Ay = 4.33 
B) Ax = 2.50 and Ay = -4.33 
C) Ax = -4.33 and Ay = -2.50 
D) Ax = -4.33 and Ay = 2.50 
E) Ax = 1.78 and Ay = -2.14 
A) Ax = 2.50 and Ay = 4.33 
B) Ax = 2.50 and Ay = -4.33 
C) Ax = -4.33 and Ay = -2.50 
D) Ax = -4.33 and Ay = 2.50 
E) Ax = 1.78 and Ay = -2.14

Question 10

For general projectile motion, which statement is true when the projectile is at the highest point of its trajectory?

Accepted Answer

A) Its acceleration is zero. 
B) Its velocity is perpendicular to the acceleration. 
C) Its velocity and acceleration are both zero. 
D) The horizontal component of its velocity is zero. 
E) The horizontal and vertical components of its velocity are zero. 
A) Its acceleration is zero. 
B) Its velocity is perpendicular to the acceleration. 
C) Its velocity and acceleration are both zero. 
D) The horizontal component of its velocity is zero. 
E) The horizontal and vertical components of its velocity are zero.

Question 11

An object has a position given by   = [2.0 m + ( 5.00 m/s)t]   + [3.0 m - ( 2.00 m/s2)t2]   . What is the magnitude of the acceleration of the object at time t = 2.00 s?

Accepted Answer

A) 1.00 m/s2  
B) 0.00 m/s2  
C) 0.722 m/s2  
D) 4.00 m/s2  
E) 2.00 m/s2  
A) 1.00 m/s2  
B) 0.00 m/s2  
C) 0.722 m/s2  
D) 4.00 m/s2  
E) 2.00 m/s2

Question 12

The vertical component of the acceleration of a projectile remains constant during the entire trajectory of the projectile.

Accepted Answer

A) True 
 B)False

Question 13

An airplane is flying at a speed of 200 m/s in level flight at an altitude of 800 m. A package is to be dropped from the airplane to land on a target on the ground. At what horizontal distance away from the target should the package be released so that it lands on the target?

Accepted Answer

A) 2.55 km 
B) 125 m 
C) 326 m 
D) 786 m 
E) 1.22 km 
A) 2.55 km 
B) 125 m 
C) 326 m 
D) 786 m 
E) 1.22 km

Question 14

A boat, whose speed in still water is 1.75 m/s, must aim upstream at an angle of 26.3° (with respect to a line perpendicular to the shore) in order to travel directly across the stream.
(a) Determine the speed of the current.
(b) Determine the resultant speed of the boat with respect to the shore.

Accepted Answer

(a) 0.775

Question 15

The magnitude of a vector can be less than the magnitude of one of its components.

Accepted Answer

A) True 
 B)False

Question 16

Under what condition is   =   +   ?

Accepted Answer

A) Vectors   and
  are in the same direction. 
B) The statement is always true. 
C) Vectors   and
  are in opposite directions. 
D) Vectors   and
  are in perpendicular directions. 
E) The statement is never true. 
A) Vectors   and
  are in the same direction. 
B) The statement is always true. 
C) Vectors   and
  are in opposite directions. 
D) Vectors   and
  are in perpendicular directions. 
E) The statement is never true.

Question 17

A child throws a ball with an initial speed of 8.00 m/s at an angle of 40.0° above the horizontal. The ball leaves her hand 1.00 m above the ground. How long is the ball in flight before it hits the ground?

Accepted Answer

A) 1.22 s 
B) 6.79 s 
C) 7.45 s 
D) 9.14 s 
E) 2.44 s 
A) 1.22 s 
B) 6.79 s 
C) 7.45 s 
D) 9.14 s 
E) 2.44 s

Question 18

Vector   has a magnitude 5.00 and points in a direction 50.0° counterclockwise from the positive x axis. What are the x and y components of vector   .

Accepted Answer

A) Ax = 0.643 and Ay = 0.766 
B) Ax = -3.83 and Ay = -3.21 
C) Ax = 3.21 and Ay = 3.83 
D) Ax = 3.83 and Ay = 3.21 
E) Ax = 0.766 and Ay = 0.643 
A) Ax = 0.643 and Ay = 0.766 
B) Ax = -3.83 and Ay = -3.21 
C) Ax = 3.21 and Ay = 3.83 
D) Ax = 3.83 and Ay = 3.21 
E) Ax = 0.766 and Ay = 0.643

Question 19

If   +   =0, then the vectors   and   have equal magnitudes and are directed in the same direction.

Accepted Answer

A) True 
 B)False

Question 20

A projectile is shot horizontally at 23.4 m/s from the roof of a building 55.0 m tall.
(a) Determine the time necessary for the projectile to reach the ground below.
(b) Determine the distance from the base of the building that the projectile lands.
(c) Determine the horizontal and vertical components of the velocity just before the projectile reaches the ground.

Accepted Answer

(a) 3.35 s
(b) 78.4

Exam 3: Kinematics in Two or Three Dimensions; Vectors

A vector has components Ax = 12 m and Ay = 5.0 m. What is the magnitude of vector ?

For general projectile motion, the horizontal component of a projectile's velocity

For a projectile launched horizontally, the vertical component of its velocity

An object has a velocity 0(t) = (3.00 m/s) + (1.00 m/s) at time t = 0.00 s. The acceleration of the object is (t) = (2.00 m/s3)t + (1.00 m/s4)t2 . If the object is located at 0(t) = (1.00 m) + (-1.00 m) at time t = 0.00 s., what is the position of the object at time t = 1.00 s?

A child throws a ball with an initial speed of 8.00 m/s at an angle of 40.0° above the horizontal. The ball leaves her hand 1.00 m above the ground. What is the magnitude of the ball's velocity just before it hits the ground?

Vector = - . Under what condition is = + ?

Vector has a magnitude 5.00 and points in a direction 60.0° clockwise from the negative y axis. What are the x and y components of vector .

For general projectile motion, which statement is true when the projectile is at the highest point of its trajectory?

An object has a position given by = [2.0 m + ( 5.00 m/s)t] + [3.0 m - ( 2.00 m/s2)t2] . What is the magnitude of the acceleration of the object at time t = 2.00 s?

The vertical component of the acceleration of a projectile remains constant during the entire trajectory of the projectile.

An airplane is flying at a speed of 200 m/s in level flight at an altitude of 800 m. A package is to be dropped from the airplane to land on a target on the ground. At what horizontal distance away from the target should the package be released so that it lands on the target?

A boat, whose speed in still water is 1.75 m/s, must aim upstream at an angle of 26.3° (with respect to a line perpendicular to the shore) in order to travel directly across the stream. (a) Determine the speed of the current. (b) Determine the resultant speed of the boat with respect to the shore.

The magnitude of a vector can be less than the magnitude of one of its components.

Under what condition is = + ?

A child throws a ball with an initial speed of 8.00 m/s at an angle of 40.0° above the horizontal. The ball leaves her hand 1.00 m above the ground. How long is the ball in flight before it hits the ground?

Vector has a magnitude 5.00 and points in a direction 50.0° counterclockwise from the positive x axis. What are the x and y components of vector .

If + =0, then the vectors and have equal magnitudes and are directed in the same direction.

Introduction, Measurement, Estimating

Describing Motion: Kinematics in One Dimension

Dynamics: Newtons Laws of Motion

Using Newtons Laws: Friction, Circular Motion, Drag Forces

Gravitation and Newtons6 Synthesis

Work and Energy

Conservation of Energy

Linear Momentum

Rotational Motion

Angular Momentum; General Rotation

Static Equilibrium; Elasticity and Fracture

Fluids

Oscillations

Wave Motion

Sound

Temperature, Thermal Expansion, and the Ideal Gas Law

Kinetic Theory of Gases

Heat and the First Law of Thermodynamics

Second Law of Thermodynamics

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Gausss Law

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Capacitance, Dielectrics, Electric Energy Storage

Electric Currents and Resistance

Dc Circuits

Magnetism

Sources of Magnetic Field

Electromagnetic Induction and Faradays Law

Inductance, Electromagnetic Oscillations, and Ac Circuits

Maxwells Equations and Electromagnetic Waves

Light: Reflection and Refraction

Lenses and Optical Instruments

The Wave Nature of Light; Interference

Diffraction and Polarization

Special Theory of Relativity

Early Quantum Theory and Models of the Atom

Quantum Mechanics

Quantum Mechanics of Atoms

Molecules and Solids

Nuclear Physics and Radioactivity

Nuclear Energy: Efects and Uses of Radiation

Elementary Particle

Astrophysics and Cosmology

Filters

A vector has components A_x = 12 m and A_y = 5.0 m. What is the magnitude of vector ?

An object has a velocity ₀(t) = (3.00 m/s) + (1.00 m/s) at time t = 0.00 s. The acceleration of the object is (t) = (2.00 m/s³)t + (1.00 m/s⁴)t² . If the object is located at ₀(t) = (1.00 m) + (-1.00 m) at time t = 0.00 s., what is the position of the object at time t = 1.00 s?

An object has a position given by = [2.0 m + ( 5.00 m/s)t] + [3.0 m - ( 2.00 m/s²)t²] . What is the magnitude of the acceleration of the object at time t = 2.00 s?