Deck 10: Motion in a Plane

Question 1

The magnitude of a vector can never be less than the magnitude of one of its components.

Answer 1

True

Question 2

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? Air resistance is small enough to be ignored.

A) He should aim it at the monkey.
B) He should aim it below the monkey.
C) He should aim it above the monkey.

Answer 2

He should aim it at the monkey.

Question 3

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

A) be behind the package.
B) be over the package.
C) be in front of the package.
D) depend of the speed of the plane when the package was released.

Answer 3

be over the package.

Question 4

For general projectile motion,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 5

If 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 about these two vectors is correct?

A) Vector is parallel to vector

B) Vectors and
point in opposite directions.
C) Vector is perpendicular to vector

D) The magnitude of vector is equal to the magnitude of vector

E) The magnitude of vector is twice the magnitude of vector

Question 6

Jan and Len throw identical rocks off a tall building at the same time.The ground near the building is flat.Jan throws her rock straight downward.Len throws his rock downward and outward such that the angle between the initial velocity of the rock and the horizon is 30°.Len throws the rock with a speed twice that of Jan's rock.If air resistance is negligible,which rock hits the ground first?

A) They hit at the same time.
B) Jan's rock hits first.
C) Len's rock hits first.
D) It is impossible to know from the information given.

Question 7

Shown below are the velocity and acceleration vectors for a person in several different types of motion.In which case is the person slowing down and turning to his right?

A)

B)

C)

D)

E)

Question 8

Under what condition is | -
| = A + B?

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) The statement is never true.

Question 9

The value of the dot product of two vectors depends on the particular coordinate system being used.

Question 10

For the vectors shown in the figure,express vector
in terms of vectors
and .

Question 11

If A > B,under what condition is | -
| = A - B?

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

Question 12

If
-
= 0,then the vectors
and
have equal magnitudes and are directed in the opposite directions from each other.

Question 13

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 14

While an object is in projectile motion (with upward being positive)with no air resistance

A) the horizontal component of its velocity remains constant and the horizontal component of its acceleration is equal to -g.
B) the horizontal component of its velocity remains constant and the vertical component of its acceleration is equal to -g.
C) the horizontal component of its velocity remains constant and the vertical component of its acceleration is equal to zero.
D) the vertical component of both its velocity and its acceleration remain constant.
E) the vertical component of its velocity remains constant and the vertical component of its acceleration is equal to -g.

Question 15

Which of the following is an accurate statement?

A) The magnitude of a vector can be zero even though one of its components is not zero.
B) It is possible to add a scalar quantity to a vector.
C) Even though two vectors have unequal magnitudes, it is possible that their vector sum is zero.
D) Rotating a vector about an axis passing through the tip of the vector does not change the vector.
E) The magnitude of a vector is independent of the coordinate system used.

Question 16

Alice and Tom dive from an overhang into the lake below.Tom simply drops straight down from the edge,but Alice takes a running start and jumps with an initial horizontal velocity of 25 m/s.Neither person experiences any significant air resistance.Just as they reach the lake below

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

Question 17

If all the components of a vector are equal to 1,then that vector is a unit vector.

Question 18

If the dot product of two nonzero vectors is zero,the vectors must be perpendicular to each other.

Question 19

Alice and Tom dive from an overhang into the lake below.Tom simply drops straight down from the edge,but Alice takes a running start and jumps with an initial horizontal velocity of 25 m/s.Neither person experiences any significant air resistance.Compare the time it takes each of them to reach the lake below.

A) Alice reaches the surface of the lake first.
B) Tom reaches the surface of the lake first.
C) Alice and Tom will reach the surface of the lake at the same time.

Question 20

If two nonzero vectors point in the same direction,their dot product must be zero.

Question 21

The components of vector are B_x = -3.5 and B_y = -9.7,and the components of vector
Are C_x = -6 and C_y = +8.1.What is the angle (less than 180 degrees)between vectors
And
?

A) 124°
B) 56°
C) 17°
D) 163°
E) 106°

Question 22

Vector has a magnitude of 75.0 cm and points at 30° above the positive x-axis. Vector has a magnitude of 25.0 cm and points along the negative x-axis. Vector
has a magnitude of 40.0 cm 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 x and y components of the sum of these three vectors.
(e)Determine the magnitude and direction of the sum of these three vectors.

Question 23

Vectors and
Are shown in the figure.Vector
Is given by
=
-
The magnitude of vector
Is 16.0 units,and the magnitude of vector
Is 7.00 units.What is the angle of vector
,measured counterclockwise from the +x-axis?

A) 16.9°
B) 22.4°
C) 73.1°
D) 287°
E) 292°

Question 24

Vector
has a magnitude of 5.5 cm and points along the x-axis. Vector
has a magnitude of 7.5 cm 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 x and y components of the sum of these two vectors.
(d)Determine the magnitude and direction of the sum of these two vectors.

Question 25

A box of mass m is pulled with a constant acceleration a along a horizontal frictionless floor by a wire that makes an angle of 15° above the horizontal.If T is the tension in this wire,then

A) T = ma.
B) T > ma.
C) T < ma.

Question 26

You walk 55 m to the north,then turn 60° to your right and walk another 45 m.How far are you from where you originally started?

A) 87 m
B) 50 m
C) 94 m
D) 46 m

Question 27

If you set the cruise control of your car to a certain speed and take a turn,the speed of the car will remain the same.Is the car accelerating?

A) Yes
B) No

Question 28

A 3.00-kg ball swings rapidly in a complete vertical circle of radius 2.00 m by a light string that is fixed at one end.The ball moves so fast that the string is always taut and perpendicular to the velocity of the ball.As the ball swings from its lowest point to its highest point

A) the work done on it by gravity and the work done on it by the tension in the string are both equal to -118 J.
B) the work done on it by gravity is -118 J and the work done on it by the tension in the string is +118 J.
C) the work done on it by gravity is +118 J and the work done on it by the tension in the string is -118 J.
D) the work done on it by gravity is -118 J and the work done on it by the tension in the string is zero.
E) the work done on it by gravity and the work done on it by the tension in the string are both equal to zero.

Question 29

The components of vector are A_x = + 3.90 and A_y = -4.00.What is the angle measured counterclockwise from the +x-axis to vector
?

A) 314°
B) 134°
C) 224°
D) 136°
E) 46.0°

Question 30

An airplane undergoes the following displacements: First,it flies 66 km in a direction 30° east of north.Next,it flies 49 km due south.Finally,it flies 100 km 30° north of west.Using vector components,determine how far the airplane ends up from its starting point.

A) 79 km
B) 81 km
C) 82 km
D) 78 km
E) 76 km

Question 31

A helicopter is flying horizontally with a speed of 444 m/s over a hill that slopes upward with a 2% grade (that is,the "rise" is 2% of the "run").What is the component of the helicopter's velocity perpendicular to the sloping surface of the hill?

A) 8.9 m/s
B) 220 m/s
C) 435 m/s
D) 444 m/s

Question 32

A small glider is coasting horizontally when suddenly a very heavy piece of cargo falls out of the bottom of the plane.You can neglect air resistance.Just after the cargo has fallen out

A) the plane speeds up and the cargo slows down.
B) the plane speeds up but the cargo does not change speed.
C) neither the cargo nor the plane change speed.
D) the cargo slows down but the plane does not change speed.
E) both the cargo and the plane speed up.

Question 33

A brick is resting on a rough incline as shown in the figure.The friction force acting on the brick,along the incline,is

A) zero.
B) equal to the weight of the brick.
C) greater than the weight of the brick.
D) less than the weight of the brick.

Question 34

The components of vector are A_x = +2.2 and A_y = -6.9,and the components of vector
Are given are B_x = -6.1 and B_y = -2.2.What is the magnitude of the vector
-
?

A) 9.5
B) 6.1
C) 9.9
D) 91
E) 0.76

Question 35

An apple falls from an apple tree growing on a 20° slope.The apple hits the ground with an impact velocity of 16.2 m/s straight downward.What is the component of the apple's impact velocity parallel to the surface of the slope?

A) 5.5 m/s
B) 8.7 m/s
C) 12 m/s
D) 15 m/s

Question 36

Vector has a magnitude 5.00 and points in a direction 40.0° clockwise from the negative y axis. What are the x and y components of vector

A) A_x = 3.83 and A_y = 3.21
B) A_x = 3.83 and A_y = -3.21
C) A_x = -3.21 and A_y = -3.83
D) A_x = -3.21 and A_y = 3.83
E) A_x = 4.29 and A_y = 2.16

Question 37

A rabbit trying to escape a fox runs north for 8.0 m,darts northwest for 1.0 m,then drops 1.0 m down a hole into its burrow.What is the magnitude of the net displacement of the rabbit?

A) 8.8 m
B) 8.1 m
C) 66 m
D) 10 m

Question 38

Vectors and
Are shown in the figure.Vector
Is given by
=
-
)The magnitude of vector
Is 16.0 units,and the magnitude of vector
Is 7.00 units.What is the magnitude of vector
?

A) 9.00
B) 9.53
C) 15.5
D) 16.2
E) 17.5

Question 39

You walk 53 m to the north,then turn 60° to your right and walk another 45 m.Determine the direction of your displacement vector.Express your answer as an angle relative to east.

A) 63° N of E
B) 50° N of E
C) 57° N of E
D) 69° N of E

Question 40

In the figure,the magnitude of vector is 18.0 units,and the magnitude of vector is 12.0 units.What vector must be added to the vectors and so that the resultant of these three vectors points in the -x direction and has a magnitude of 7.50 units? Use vector components to find your answer,and express vector by giving its magnitude and the angle it makes with the +x-axis taking counterclockwise to be positive.

Question 41

The angle between vector = 2.00
+ 3)00
And vector
Is 45.0°. The scalar product of vectors
And
Is 3.00. If the x component of vector
Is positive,what is vector

A)
B)
C)
D)
E)

Question 42

Determine the scalar product of = 6.0
+ 4)0
- 2)0
And
= 5)0
- 6)0
- 3)0

A) 30 + 24
+ 6

B) 30 - 24
+ 6

C) 12
D) 60
E) undefined

Question 43

If = 3 - + 4 and = x + - 5 ,find x so will be perpendicular to

Question 44

Two boys searching for buried treasure are standing underneath the same tree.One boy walks 18 m east and then 18 m north. The other boy walks 16 m west and then 11 m north. Find the scalar product of their net displacements from the tree.

Question 45

What is the angle between the vector = +3
- 2
- 3
And the +y-axis?

A) 115°
B) 65°
C) 25°
D) 155°
E) 90°

Question 46

Three forces are exerted on an object placed on a tilted floor.Forces are vectors.The three forces are directed as shown in the figure. If the forces have magnitudes F₁ = 1.0 N,F₂ = 8.0 N and F₃ = 7.0 N, where N is the standard unit of force,what is the component of the net force _net =
₁ +
₂ +
₃ parallel to the floor?

A) 2.5 N
B) 5.1 N
C) 6.0 N
D) 7.8 N

Question 47

Vectors and
Are shown in the figure. What is
?

A) 31.8
B) -32.0 - 2.00

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

Question 48

As shown in the figure,three force vectors act on an object.The magnitudes of the forces as shown in the figure are F₁ = 80.0 N,F₂ = 60.0 N,and F₃ = 40.0 N,where N is the standard SI unit of force.The resultant force acting on the object 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 49

Determine the angle between the directions of vector = 3.00
+ 1)00
And vector
= -3.00
+ 3)00

A) 26.6°
B) 30.0°
C) 88.1°
D) 117°
E) 45.2°

Question 50

For the vectors shown in the figure,assume numbers are accurate to two significant figures. The scalar product ×
Is closest to

A) zero.
B) 16.
C) 45.
D) -16.
E) -45.

Question 51

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


All quantities are SI units.What is the distance between object A and object B at time t = 3.00 s?

A) 34.6 m
B) 15.0 m
C) 18.3 m
D) 3.46 m
E) 29.8 m

Question 52

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,Jane physics student quickly adds the displacements and walks in a straight line to find the treasure. How far and in what direction does Jane 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 53

The scalar product of vector = 3.00
+ 2)00
And vector
Is 10.0. Which of the following vectors could be vector
?

A) 2.00 + 4.00

B) 4.00 + 6.00

C) 5.00 + 4.00

D) 12.0
E) 2.00 + 2.00

Question 54

A rectangular box is positioned with its vertices at the following points:
A = (0,0,0) C = (2,4,0) E = (0,0,3) G = (2,4,3)
B = (2,0,0) D = (0,4,0) F = (2,0,3) H = (0,4,3)
If the coordinates all have three significant figures,the angle between the line segments AG and AH is closest to:

A) 21.8°.
B) 22.5°.
C) 26.6°.
D) 36.9°.
E) 45.0°.

Question 55

What is the magnitude of +
+
,where
= 1)00
+ 4)00
- 1)00 ,
= 3)00
- 1)00
- 4)00
And
= -1.00
+ 1)00
?

A) 7.07
B) 2.00
C) 10.76
D) 6.78
E) 8.12

Question 56

If = +4
- 2
- 3
And
= -4
-2
- 3
,which of the following numbers is closest to the magnitude of
-
?

A) 8
B) 7
C) 9
D) 10
E) 11

Question 57

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 58

An object has a position given by = [2.0 m + (5.00 m/s)t]
+ [3.0 m - (2.00 m/s²)t²]
,where quantities are in SI units.What is the speed of the object at time t = 2.00 s?

A) 6.40 m/s
B) 9.43 m/s
C) 7.00 m/s
D) 7.65 m/s
E) 13.0 m/s

Question 59

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 60

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 61

A hobby rocket reaches a height of 72.3 m and lands 111 m from the launch point with no air resistance.What was the angle of launch?

A) 69.0°
B) 67.4°
C) 22.6°
D) 44.8°

Question 62

An object has a position given by = [2.0 m + (3.00 m/s)t]
+ [3.0 m - (2.00 m/s²)t²]
,where all quantities are in SI units.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) 0.522 m/s²
D) 4.00 m/s²
E) 2.00 m/s²

Question 63

A hockey puck slides off the edge of a table with an initial velocity of 28.0 m/s.and experiences no air resistance.The height of the tabletop above the ground is 2.00 m.What is the angle below the horizontal of the velocity of the puck just before it hits the ground?

A) 77.2°
B) 72.6°
C) 12.8°
D) 12.6°
E) 31.8°

Question 64

An electron moves with a constant horizontal velocity of 3.0 × 10⁶ m/s,and no initial vertical velocity as it enters a deflector inside a TV tube.The electron strikes the screen after traveling 17.0 cm.horizontally and 40.0 cm vertically upward with no horizontal acceleration.What is the constant vertical acceleration provided by the deflector? (The effects of gravity can be ignored.)

A) 2.5 × 10¹⁴ m/s²
B) 8.3 × 10² m/s²
C) 1.4 × 10⁴ m/s²
D) 1.2 × 10¹⁴ m/s²

Question 65

A rock is thrown at a window that is located 18.0 m above the ground. The rock is thrown at an angle of 40.0° above horizontal. The rock is thrown from a height of 2.00 m above the ground with a speed of 30.0 m/s and experiences no appreciable air resistance. If the rock strikes the window on its upward trajectory,from what horizontal distance from the window was it released?

A) 53.2 m
B) 48.7 m
C) 71.6 m
D) 29.8 m
E) 27.3 m

Question 66

A plane flying at 70.0 m/s suddenly stalls.If the acceleration during the stall is 9.8 m/s² directly downward,the stall lasts 5.0 s,and the plane was originally climbing at 25° to the horizontal,what is the velocity after the stall?

A) 66 m/s at 17° below the horizontal
B) 66 m/s at 17° above the horizontal
C) 80 m/s at 37° below the horizontal
D) 80 m/s at 37° above the horizontal

Question 67

A projectile is fired from point 0 at the edge of a cliff,with initial velocity components of v_0x = 60.0 m/s and v_0y = 175 m/s,as shown in the figure.The projectile rises and then falls into the sea at point P.The time of flight of the projectile is 40.0 s,and it experiences no appreciable air resistance in flight.What is the height of the cliff?

Question 68

A catapult is tested by Roman legionnaires.They tabulate the results in a papyrus and 2000 years later the archaeological team reads (distances translated into modern units): Range = 0.20 km;
Angle of launch = π/4; landing height = launch height.What is the initial velocity of launch of the boulders if air resistance is negligible?

A) 44 m/s
B) 1.4 m/s
C) 22 m/s
D) 0.69 m/s

Question 69

A hockey puck slides off the edge of a table at point A with an initial velocity of 20.0 m/s and experiences no air resistance.The height of the tabletop above the ground is 2.00 m.
(a)What is the speed (not the velocity)of the puck just before it touches the ground?
(b)What is the distance between point A and the point where the puck hits the ground?

Question 70

A hiker throws a stone from the upper edge of a vertical cliff.The stone's initial velocity is 25.0 m/s directed at 40.0° with the face of the cliff,as shown in the figure.The stone hits the ground 3.75 s after being thrown and feels no appreciable air resistance as it falls.
(a) What is the height of the cliff?
(b) How far from the foot of the cliff does the stone land?
(c) How fast is the stone moving just before it hits the ground?

Question 71

What is the maximum distance we can shoot a dart,from ground level,provided our toy dart gun gives a maximum initial velocity of 2.78 m/s and air resistance is negligible?

A) 0.789 m
B) 1.58 m
C) 1.39 m
D) 0.394 m

Question 72

An airplane is flying at a speed of 2.00 × 10² m/s in level flight at an altitude of 8.00 × 10² m. A package is to be dropped from the airplane to land on a target on the ground.Ignore air resistance.
(a) At what horizontal distance away from the target should the package be released so that it lands on the target?
(b) In what direction relative to the horizontal will the package be traveling when it hits the ground?

Question 73

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 and experience negligible air resistance.
(a) What is the magnitude of the ball's velocity just before it hits the ground?
(b) At what angle below the horizontal does the ball approach the ground?

Question 74

A ball is thrown at a 60.0° angle above the horizontal across level ground. It is thrown from a height of 2.00 m above the ground with a speed of 20.0 m/s and experiences no appreciable air resistance.The time the ball remains in the air before striking the ground is closest to

A) 16.2 s.
B) 3.07 s.
C) 3.32 s.
D) 3.53 s.
E) 3.64 s.

Question 75

A projectile is fired from point 0 at the edge of a cliff,with initial velocity components of v_0x= 60 m/s and v_0y = 175 m/s,as shown in the figure.The projectile rises and then falls into the sea at point P.The time of flight of the projectile is 40.0 s,and it experiences no appreciable air resistance in flight.What is the magnitude of the velocity of the projectile 21.0 s after it is fired?

Question 76

The horizontal coordinates of a Frisbee
in a strong wind are given by where x and y are in meters,and t is in seconds.
(a)What is the acceleration of the Frisbee? Give a magnitude and a direction,measuring angles from the positive x direction.
(b)What is the magnitude of the velocity at t = 2.0 s,accurate to the nearest m/s?

Question 77

A rescue plane flying horizontally at 72.6 m/s spots a survivor in the ocean 182 m directly below and releases an emergency kit with a parachute.Because of the shape of the parachute,it experiences insignificant horizontal air resistance.If the kit descends with a constant vertical acceleration of 5.82 m/s²,how far away from the survivor will it hit the waves?

A) 574 m
B) 4.54 km
C) 406 m
D) 602 m

Question 78

A projectile returns to its original height 4.08 s after being launched,during which time it travels 76.2 m horizontally.If air resistance can be neglected,what was the projectile's initial speed?

Question 79

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 and experience negligible air resistance.
(a) How far from where the child is standing does the ball hit the ground?
(b) How long is the ball in flight before it hits the ground?

Question 80

A boy throws a rock with an initial velocity of 2.15 m/s at 30.0° above the horizontal.If air resistance is negligible,how long does it take for the rock to reach the maximum height of its trajectory?

A) 0.110 s
B) 0.194 s
C) 0.215 s
D) 0.303 s