Deck 3: Kinematics in Two or Three Dimensions; Vectors

Question 1

A projectile is launched with velocity v at an angle θ above the horizontal. The range of the projectile does not depend upon the acceleration due to gravity at that location.

Answer 1

False

Question 2

Under what condition is = + ?

A)The magnitude of vector is zero.
B)Vectors and
are in opposite directions.
C)Vectors and
are in the same direction.
D)Vectors and
are in perpendicular directions.
E)both A and B

Answer 2

both A and B

Question 3

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

Answer 3

False

Question 4

A projectile is launched from ground level with a certain speed. For any range less than the maximum range there are two possible launch angles that give the same range.

Question 5

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

Question 6

If - = and A-B=C, then the vectors and are oriented perpendicular relative to one other.

Question 7

The horizontal component of the velocity of a projectile remains constant during the entire trajectory of the projectile.

Question 8

If + = and A+B=C, then the vectors and are oriented perpendicular relative to one other.

Question 9

The sum of two vectors has the greatest magnitude when the angle between these two vectors is

A)90°.
B)180°.
C)60°.
D)0°.
E)270°.

Question 10

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

Question 11

If + = and A² + B² = C², then the vectors and are oriented perpendicular relative to one other.

Question 12

If the magnitude of vector is less than the magnitude of vector , then the x component of is less than the x component of .

Question 13

Vector quantities are represented in terms of their magnitude and direction.

Question 14

Vector = - . Under what condition is = + ?

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 15

The magnitude of a unit vector is one.

Question 16

Under what condition is = + ?

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

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

Question 18

A student adds two displacement vectors that have the magnitudes of 14.0 m and 6.0 m. What is the range of possible answers for the magnitude of the resultant vector?

Question 19

Vector = + . Under what condition is = + ?

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

Question 20

Under what condition is = - ?

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

Question 21

A pilot drops a bomb from a plane flying horizontally at a constant speed. Neglecting air resistance, when the bomb hits the ground the horizontal location of the plane will

A)be behind the bomb.
B)be over the bomb.
C)be in front of the bomb.
D)depend of the speed of the plane when the bomb was released.
E)depend of the mass of the bomb when it was released.

Question 22

A monkey is sitting at the top of a tree 20 m above ground level. A person standing on the ground wants to feed the monkey. He uses a bow and arrow to launch the food to the monkey. If the monkey remains seated at the top of the tree, how should the person aim the arrow containing the food so that the monkey gets the food?

A)He should aim it at the monkey.
B)He should aim it below the monkey.
C)He should aim it above the monkey.
D)None of the other choices is correct.

Question 23

FIGURE 3-1
Refer to Fig. 3-1. The components of vectors and are

A)A_x = 0 B_x = B sin 30° A_y = 0 B_y = B cos30°.
B)A_x = A sin90° B_x = B cos60° A_y = A cos90° B_y = B sin60°.
C)A_x = A cos0° B_x = -B cos60° A_y = A cos90° B_y = B cos30°.
D)A_x = A cos90° B_x = B sin60° A_y = A sin90° B_y = B cos60°.
E)A_x = A cos90° B_x = 0 A_y = A sin90° B_y = 0

Question 24

A monkey is sitting at the top of a tree 20 m above ground level. A person standing on the ground wants to feed the monkey. He uses a bow and arrow to launch the food to the monkey. If the person knows that the monkey is going to drop from the tree at the same instant that the person launches the food, how should the person aim the arrow containing the food?

A)He should aim it at the monkey.
B)He should aim it below the monkey.
C)He should aim it above the monkey.
D)None of the other choices is correct.

Question 25

The eastward component of vector is equal to the westward component of vector and their northward components are equal. Which one of the following statements is correct for these two vectors?

A)Vector is parallel to vector
.
B)Vector is anti-parallel to vector
.
C)Vector is perpendicular to vector
.
D)Magnitude of vector is equal to the magnitude of vector
.
E)Magnitude of vector is twice the magnitude of vector
.

Question 26

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

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

Question 27

When a football in a field goal attempt reaches its maximum height, how does its speed compare to its initial speed?

A)It is zero.
B)It is less than its initial speed.
C)It is equal to its initial speed.
D)It is greater than its initial speed.
E)Cannot be determined without additional information.

Question 28

Refer to Fig. 3-2. Vector as expressed in terms of vectors and is given by

A) +
.
B) -
.
C) .
D) .
E)None of the other choices is correct.

Question 29

A ball rolls off the edge of a table. The horizontal component of the ball's velocity remains constant during its entire trajectory because

A)the ball is not acted upon by any force.
B)the net force acting on the ball is zero.
C)the ball is not acted upon by a force in the horizontal direction.
D)the ball is not acted upon by a force in the vertical direction.
E)None of the other choices is correct.

Question 30

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

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

Question 31

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

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 32

The resultant vector of two vectors and will have the minimum value when the angle between these vectors is which one of the following?

A)0°.
B)90°.
C)270°
D)180°
E)360°

Question 33

James and John dive from an overhang into the lake below. James simply drops straight down from the edge. John takes a running start and jumps with an initial horizontal velocity of 25 m/s. Compare the time it takes each to reach the lake below.

A)James reaches the surface of the lake first.
B)John reaches the surface of the lake first.
C)James and John will reach the surface of the lake at the same time.
D)Cannot be determined without knowing the mass of both James and John.
E)Cannot be determined without knowing the weight of both James and John.

Question 34

James and John dive from an overhang into the lake below. James simply drops straight down from the edge. John takes a running start and jumps with an initial horizontal velocity of 25 m/s. When they reach the lake below,

A)the splashdown speed of James is larger than that of John.
B)the splashdown speed of John is larger than that of James.
C)they will both have the same splashdown speed.
D)the splashdown speed of James will always be 9.8 m/s larger than that of John.
E)the splashdown speed of John will always be 25 m/s larger than that of John.

Question 35

For general projectile motion, the vertical component of a projectile's acceleration

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

Question 36

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

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

Question 37

An Olympic athlete throws a javelin at four different angles above the horizontal, each with the same speed: 30°, 40°, 60°, and 80°. Which two throws cause the javelin to land the same distance away?

A)30° and 80°
B)40° and 60°
C)30° and 40°
D)40° and 80°
E)30° and 60°

Question 38

A student kicks a soccer ball in a high arc toward the opponent's goal. At the highest point in its trajectory:

A)both velocity and acceleration of the soccer ball are zero.
B)neither the ball's velocity nor its acceleration is zero.
C)the ball's acceleration is zero but not its velocity.
D)the ball's acceleration points upwards.
E)the ball's velocity points downwards.

Question 39

FIGURE 3-2
Refer to Fig. 3-2. Vector as expressed in terms of vectors and is given by

A) +
.
B) -
.
C) .
D) .
E)None of the other choices is correct.

Question 40

For a projectile launched horizontally, the horizontal component of a projectile's velocity

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

Question 41

Vector = 4.00 m points eastward and vector = 3.00 m points northward. The resultant vector + is given by

A)5.00 m at an angle 71.6° north of east.
B)5.00 m at an angle 36.9° north of east.
C)5.00 m at an angle 53.1° north of east.
D)5.00 m at an angle 18.4° north of east.
E)5.00 m at an angle 26.6° north of east.

Question 42

Vector = -1.00 + 2.00 and vector = 3.00 + 4.00 . What are the magnitude and direction of vector = + ?

A)6.32 in a direction 71.6° counterclockwise from the positive x axis
B)8.00 in a direction 71.6° counterclockwise from the positive x axis
C)8.00 in a direction 18.4° counterclockwise from the positive x axis
D)6.32 in a direction 18.4° counterclockwise from the positive x axis
E)40 in a direction 18.4° counterclockwise from the positive x axis

Question 43

Vector = 1.00 + -2.00 and vector = 3.00 + 4.00 . What are the magnitude and direction of vector = + ?

A)7.21 in a direction 33.7° counterclockwise from the positive x axis
B)6.00 in a direction 63.4° counterclockwise from the positive x axis
C)4.47 in a direction 6.34° counterclockwise from the positive x axis
D)4.47 in a direction 26.6° counterclockwise from the positive x axis
E)7.21 in a direction 56.3° counterclockwise from the positive x axis

Question 44

You are trying to cross a river that flows due south with a strong current. You start out in your motorboat on the west bank desiring to reach the east bank directly east from your starting point. You should head your motorboat

A)due east.
B)due north.
C)due south.
D)in a southeasterly direction.
E)in a northeasterly direction.

Question 45

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.

Question 46

Vector = -2.00 + 3.00 . Determine the magnitude and direction of vector .

A)3.61 in a direction 304° counterclockwise from the positive x axis
B)3.61 in a direction 56.3° counterclockwise from the positive x axis
C)-1.00 in a direction 56.3° counterclockwise from the positive x axis
D)3.61 in a direction 124° counterclockwise from the positive x axis
E)5.00 in a direction 56.3° counterclockwise from the positive x axis

Question 47

Vector = 3.00 + -1.00 and vector = 3.00 + 4.00 . What is vector = 2.00 + 3.00 ?

A)3.00 + 6.00

B)5.00 + 1.00

C)-3.00 + 9.00

D)15.0 + 10.0

E)2.00 + 3.00

Question 48

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 .

A)A_x = 0.643 and A_y = 0.766
B)A_x = -3.83 and A_y = -3.21
C)A_x = 3.21 and A_y = 3.83
D)A_x = 3.83 and A_y = 3.21
E)A_x = 0.766 and A_y = 0.643

Question 49

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.

Question 50

Vector = 4.0 m points eastward and vector = 3.0 m points westward. The resultant vector + is given by

A)7.0 m east.
B)7.0 m west.
C)1.0 m east.
D)1.0 m west.
E)3.5 m west.

Question 51

A vector has components A_x = 12.0 m and A_y = 5.00 m. What is the angle that vector makes with the x-axis?

A)12.6°
B)22.6°
C)32.6°
D)67.4°
E)6.6°

Question 52

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.

Question 53

Vector = -3.00 + 3.00 and vector = 3.00 + 4.00 . What is vector = + ?

A)0.00 + 3.00

B)7.00 + 7.00

C)-3.00 + 7.00

D)0.00 + 7.00

E)-3.00 + -3.00

Question 54

Vector = 2.00 + -1.00 and vector = 3.00 + 4.00 . What is vector = - ?

A)1.00 + 5.00

B)1.00 + 3.00

C)-1.00 + -3.00

D)-1.00 + 3.00

E)-1.00 + -5.00

Question 55

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.

Question 56

A package of supplies is dropped from a plane, and one second later a second package is dropped. Neglecting air resistance, the distance between the falling packages will

A)be constant.
B)decrease.
C)increase.
D)depend on their weight.
E)depend on the speed of the plane.

Question 57

Vector = 4.00 m points eastward and vector = 3.00 m points southward. The resultant vector + is given by

A)5.00 m at an angle 36.9° south of east.
B)5.00 m at an angle 53.1° south of east.
C)5.00 m at an angle 71.6° south of east.
D)5.00 m at an angle 18.4° south of east.
E)5.00 m at an angle 26.6° south of east.

Question 58

Vector is 5.5 cm long and points along the x axis. Vector is 7.5 cm long and points at +30° above 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 sum of these two vectors in terms of components.
(d) Determine the sum of these two vectors in terms of magnitude and direction.

Question 59

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

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

Question 60

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 .

A)A_x = 2.50 and A_y = 4.33
B)A_x = 2.50 and A_y = -4.33
C)A_x = -4.33 and A_y = -2.50
D)A_x = -4.33 and A_y = 2.50
E)A_x = 1.78 and A_y = -2.14

Question 61

FIGURE 3-5
Refer to Fig. 3-5. The components of the sum of these vectors are given by

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

Question 62

FIGURE 3-5
Refer to Fig. 3-5. The sum of these vectors is given by

A)4.2 cm at an angle 180° with respect to +x-axis.
B)4.2 cm along the y-axis.
C)4.2 cm at an angle 270° with respect to +x-axis.
D)4.2 cm along the x-axis.
E)4.2 cm along the negative y-axis.

Question 63

FIGURE 3-3
Vector = 6.0 m and points 30° north of east. Vector = 4.0 m and points 30° south of west. The resultant vector + is given by

A)2.0 m at an angle 30° north of east.
B)2.0 m at an angle 60° north of east.
C)10.0 m at an angle 60° east of north.
D)10.0 m at an angle 30° north of east.
E)10.0 m at an angle 60° north of east.

Question 64

A projectile is launched from ground level at an angle of 50.0° above horizontal with a speed of 30.0 m/s. If the projectile is moving over level ground, how long is it in the air before it again contacts the ground?

A)8.12 s
B)2.35 s
C)4.69 s
D)6.44 s
E)11.3 s

Question 65

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?

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 66

An object has a position given by = [2.0 m + ( 5.0 m/s)t] + [3.0 m - ( 1.0 m/s²)t²] . Determine the velocity of the object as a function of time.

A)5.4 m/s
B)5.1 m/s
C)( 5.0 m/s) - [( 1.0 m/s²)t]
D)( 5.0 m/s) - [( 2.0 m/s²)t]
E)( 5.0 m/s) - ( 1.0 m/s²)

Question 67

FIGURE 3-3
Vectors and are shown in Fig. 3-3. What is ?

A)31.8
B)-32.0 + -2.00

C)1028
D)34.0
E)-2.00 + -32.0

Question 68

An object has a position given by = [2.0 m + ( 3.00 m/s)t] + [3.0 m - ( 2.00 m/s²)t²] . What is the speed of the object at time t = 2.00 s?

A)5.00 m/s
B)8.54 m/s
C)5.50 m/s
D)4.65 m/s
E)11.0 m/s

Question 69

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)( 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 70

Vector = 2.00 + 2.00 and vector = 3.00 + 4.00 . What is vector = 3.00 - ?

A)-3.00 + -18.0

B)9.00 + 10.0

C)3.00 + 2.00

D)-3.00 + -2.00

E)3.00 + 18.0

Question 71

A car moves from the point (3.0 m)^x + (5.0 m)^y to the point (8.0 m)^x - (7.0 m)^y in 2.0 s. What is the magnitude of the average velocity of the car?

A)6.5 m/s
B)13 m/s
C)9.0 m/s
D)4.5 m/s
E)3.3 m/s

Question 72

A car is moving with a velocity (3.0 m/s)^x + (1.0 m/s)^y and 3.0 seconds later its velocity is (6.0 m/s)^x - (3.0 m/s)^y. What is the direction of the average acceleration of the car?

A)67° from the x-axis
B)-67° from the x-axis
C)53° from the x-axis
D)-53° from the x-axis
E)60° from the x-axis

Question 73

FIGURE 3-4
Refer to Fig. 3-4 The magnitudes of the forces as shown in the figure are: = 80.0 N, = 60.0 N, and = 40.0 N. The resultant force acting on the particle O is given by

A)180 N at an angle 60.0° with respect to +x-axis.
B)60.0 N at an angle 90.0° with respect to +x-axis.
C)20.0 N at an angle 34.3° with respect to +x-axis.
D)35.5 N at an angle 34.3° with respect to +x-axis.
E)40.0 N at an angle 60.0° with respect to +x-axis.

Question 74

A car moves from the point (3.0 m)^x + (5.0 m)^y to the point (8.0 m)^x - (7.0 m)^y in 2.0 s. What is the direction of the average velocity of the car?

A)67° from the x-axis
B)-67° from the x-axis
C)33° from the x-axis
D)-33° from the x-axis
E)52° from the x-axis

Question 75

A car is moving with a velocity (3.0 m/s)^x + (1.0 m/s)^y and 2.5 seconds later its velocity is (6.0 m/s)^x - (3.0 m/s)^y. What is the magnitude of the average acceleration of the car?

A)0.82 m/s²
B)1.6 m/s²
C)2.0 m/s²
D)4.5 m/s²
E)6.2 m/s²

Question 76

FIGURE 3-3
Vector = 6.0 m and points 30° north of east. Vector = 4.0 m and points 30° west of south. The resultant vector + is given by

A)2.7 m at an angle 8.3° south of east.
B)2.7 m at an angle 8.3° east of south.
C)3.2 m at an angle 8.3° east of south.
D)3.2 m at an angle 8.3° south of east.
E)2.3 m at an angle 8.3° south of east.

Question 77

A teacher sends her students on a treasure hunt. She gives the following instructions: 1. Walk 300 m north
2. Walk 400 m northwest
3. Walk 700 m east-southeast and the treasure is buried there.
As all the other students walk off following the instructions, Joe physics student quickly adds the displacements and walks in a straight line to find the treasure. How far and in what direction does Joe need to walk?

A)187 m in a direction 67.3° north of east
B)481 m in a direction 40.9° north of east
C)399 m in a direction 52.5° north of east
D)284 m in a direction 28.2° west of north
E)The treasure position cannot be reached in one straight walk.

Question 78

Object A has a position as a function of time given by _A(t) = (3.00 m/s)t + (1.00 m/s²)t²
. Object B has a position as a function of time given by _B(t) = (4.00 m/s)t + (-1.00 m/s²)t²

. What is the distance between object A and object B at time t = 5.00 s?

A)34.6 m
B)45.0 m
C)50.2 m
D)3.46 m
E)29.8 m

Question 79

Vector = -1.00 + -2.00 and vector = 3.00 + 4.00 . What are the magnitude and direction of vector = 3.00 + 2.00 ?

A)3.61 in a direction -56.3° counterclockwise from the positive x axis
B)3.61 in a direction 56.3° counterclockwise from the positive x axis
C)3.61 in a direction 33.7° counterclockwise from the positive x axis
D)5.00 in a direction 56.3° counterclockwise from the positive x axis
E)6.72 in a direction 34.4° counterclockwise from the positive x axis

Question 80

A projectile is launched from ground level at an angle of 70.0° above horizontal with a speed of 50.0 m/s. If the projectile is moving over level ground, how far way from the launch position does it contact the ground?

A)164 m
B)54.2 m
C)203 m
D)102 m
E)12.4 m