Deck 3: Vectors and Two-Dimensional Motion

Question 1

In a 2-dimensional Cartesian system,the x-component of a vector is known,and the angle between vector and x-axis is known.Which operation is used to calculate the magnitude of the vector? (taken with respect to the x-component)

A) dividing by cosine
B) dividing by sine
C) multiplying by cosine
D) multiplying by sine

Answer 1

dividing by cosine

Question 2

A car is initially moving at 20 m/s east,and a little while later it is moving at 10 m/s north.Which of the following best describes the orientation of the average acceleration during this time interval?

A) northeast
B) northwest
C) west
D) north of west

Answer 2

north of west

Question 3

An object moves at a constant velocity of 16 m/s to the southwest for an interval of 30 s.Halfway through this interval,what is the magnitude of its instantaneous velocity?
​

A) It can be any value from 0 to 32 m/s.
B) 16 m/s
C) 8 m/s
D) More information is needed.
E) ​32 m/s

Answer 3

16 m/s

Question 4

Which of the following is an example of a vector quantity?

A) velocity
B) temperature
C) volume
D) mass

Question 5

The following force vectors act on an object: i)55.0 newtons at 45.0° north of east and ii)25.0 newtons at 30.0° south of east.Which of the following represents the magnitude of the resultant and its angle relative to the easterly direction?
​

A) 80.0 newtons 7.50°
B) 66 newtons 23.6°
C) 66 newtons 71.5°
D) ​54.2 newtons 56.8°
E) ​79.4 newtons 40.3°

Question 6

When three vectors are added graphically and form a closed triangle,the largest enclosed angle between any two of the vectors cannot be greater than

A) 60°.
B) 90°.
C) 180°.
D) No maximum exists.

Question 7

An object,initially moving in the negative x-direction,is subjected to a change in velocity in the positive y-direction.If the resulting velocity vector is drawn from the origin,into which quadrant does this vector point?

A) 1^st
B) 2^nd
C) 3^rd
D) None,since the object is now moving in the y-direction.

Question 8

A student adds two vectors with magnitudes of 230 and 40.Which one of the following is the only possible choice for the magnitude of the resultant?

A) 280
B) 230
C) 115
D) 40
E) ​180

Question 9

A runner circles a track of radius 100 m one time in 100 s at a constant rate.The greatest change in his velocity from his starting velocity:

A) occurs one-fourth of the way around the track.
B) occurs one-half of the way around the track.
C) occurs three-fourths of the way around the track.
D) Both a and c are correct.

Question 10

In a 2-dimensional Cartesian coordinate system the y-component of a given vector is equal to that vector's magnitude multiplied by which trigonometric function,with respect to the angle between vector and y-axis?

A) sine
B) cosine
C) tangent
D) cotangent

Question 11

Find the resultant of the following two vectors: i)40 units due east and ii)100 units 30° north of west.
​

A) 100 units 30° north of west
B) 68 units 17° north of west
C) 136 units 43° north of west
D) 68 units 47° north of west
E) ​87 units 133° north of west

Question 12

In a 2-dimensional Cartesian coordinate system the x-component of a given vector is equal to that vector's magnitude multiplied by which trigonometric function,with respect to the angle between vector and x-axis?

A) sine
B) cosine
C) tangent
D) cotangent

Question 13

When we subtract a velocity vector from another velocity vector,the result is

A) another velocity.
B) an acceleration.
C) a displacement.
D) a scalar.

Question 14

A taxicab moves five blocks due north,six blocks due east,and another three blocks due north.Assume all blocks are of equal size.What is the magnitude of the taxi's displacement,start to finish?
​

A) 14 blocks
B) 6.7 blocks
C) 7.8 blocks
D) 10 blocks
E) 8​ blocks

Question 15

The first displacement is 8 m,and the second displacement is 4 m.They cannot add together to give a total displacement of:
​

A) 3 m.
B) 4 m.
C) 5 m.
D) 6 m.
E) ​7 m.

Question 16

Vector Is 2 m long,and vector Is 4 m long.The length of the sum of the vectors must be
​

A) 5 m.
B) 6 m.
C) 11 m.
D) some value from 2 m to 6 m.
E) ​2 m.

Question 17

When we add a displacement vector to another displacement vector,the result is

A) a velocity.
B) an acceleration.
C) another displacement.
D) a scalar.

Question 18

A hiker walks 200 m west and then walks 100 m north.In what direction is her resulting displacement?

A) north
B) west
C) northwest
D) None of the answers is correct.

Question 19

Vector Points north,and vector Points east.If=−,then vector11ec8726_cf4b_540b_8f60_37bcf0a2cf5d_TB34225555_11 Points

A) north of east.
B) south of east.
C) north of west.
D) south of west.

Question 20

Which type of quantity is characterized by both magnitude and direction?

A) scalar
B) vector
C) trigonometric
D) algebraic variable

Question 21

Arvin the Ant is on a picnic table.He travels 35 cm eastward,then 20 cm northward,and finally 5 cm westward.What is the magnitude of Arvin's net displacement?
​

A) 60 cm
B) 45 cm
C) 40 cm
D) 36 cm
E) ​21 cm

Question 22

I walk five miles in a straight line in a direction north of east,and I end up three miles east and several miles north.How many degrees north of east have I walked?
​

A) 37°
B) 45°
C) 31°
D) 53°
E) ​59°

Question 23

Vector Is 3.0 units in length and points along the positive x-axis;vector Is 8.0 units in length and points along a direction 150° from the positive x-axis.What is the magnitude of the resultant when vectors And Are added?
​

A) 7
B) 6.7
C) 10.7
D) 5.6
E) ​11

Question 24

A ball is rolled horizontally off a table with an initial speed of 0.28 m/s.A stopwatch measures the ball's trajectory time from table to the floor to be 0.33 s.What is the height of the table? (g = 9.8 m/s² and air resistance is negligible)
​

A) 0.63 m
B) 0.44 m
C) 0.02 m
D) 0.53 m
E) ​0.55 m

Question 25

A baseball is thrown by the center fielder (from shoulder level)to home plate where it is caught (on the fly at shoulder level)by the catcher.At what point is the magnitude of the acceleration at a minimum? (air resistance is negligible)

A) just after leaving the center fielder's hand
B) just before arriving at the catcher's mitt
C) at the top of the trajectory
D) acceleration is constant during entire trajectory

Question 26

A string attached to an airborne kite is maintained at an angle of 49° with the horizontal.If a total of 170 m of string is reeled in while bringing the kite back to the ground,what is the horizontal displacement of the kite in the process? (Assume the kite string doesn't sag. )
​

A) 128 m
B) 85 m
C) 32 m
D) 112 m
E) ​196 m

Question 27

A ball is rolled horizontally off a table with an initial speed of 0.22 m/s.A stop watch measures the ball's trajectory time from table to the floor to be 0.2 s.How far away from the table does the ball land? (g = 9.8 m/s² and air resistance is negligible)
​

A) 0.24 m
B) 0.044 m
C) 0.392 m
D) 0.152 m
E) ​0.088 m

Question 28

A baseball is thrown by the center fielder (from shoulder level)to home plate where it is caught (on the fly at an equal shoulder level)by the catcher.At what point is the ball's speed at a minimum? (air resistance is negligible)

A) just after leaving the center fielder's hand
B) just before arriving at the catcher's mitt
C) at the top of the trajectory
D) speed is constant during entire trajectory

Question 29

A baseball is thrown by the center fielder (from shoulder level)to home plate where it is caught (on the fly at shoulder level)by the catcher.At what point does the magnitude of the vertical component of velocity have its minimum value? (air resistance is negligible)

A) just after leaving the center fielder's hand
B) just before arriving at the catcher's mitt
C) at the top of the trajectory
D) magnitude of vertical component of velocity is constant

Question 30

A helicopter is traveling at 50 m/s at a constant altitude of 100 m over a level field.If a wheel falls off the helicopter,with what speed will it hit the ground? (g = 9.8 m/s² and air resistance negligible)
​

A) 59 m/s
B) 45 m/s
C) 67 m/s
D) ​4,460 m/s
E) ​57 m/s

Question 31

Arvin the Ant travels 35 cm eastward,then 20 cm northward,and finally 10 cm westward.What is Arvin's direction of displacement with respect to his original position?
​

A) 39° N of E
B) 141° N of E
C) 51° N of W
D) 30° N of E
E) ​63° N of E

Question 32

A baseball thrown from the outfield is released from shoulder height at an initial velocity of 29.1 m/s at an initial angle of 45° with respect to the horizontal.What is the maximum vertical displacement that the ball reaches during its trajectory?
​

A) 21.6 m
B) 43.2 m
C) 64.8 m
D) 43.2 m.
E) 86.4 m

Question 33

Jack pulls a sled across a level field by exerting a force of 110 N at an angle of 30° with the ground.What are the parallel and perpendicular components,respectively,of this force with respect to the ground?​

A) 190 N,110 N
B) 110 N,190 N
C) 95 N,55 N
D) 55 N,95 N
E) ​64 N,191 N

Question 34

John throws a baseball from the outfield from shoulder height,at an initial velocity of 29.7 m/s at an initial angle of 45.0° with respect to the horizontal.The ball is in its trajectory for a total interval of 4.00 s before the third baseman catches it at an equal shoulder-height level.(Assume air resistance negligible. )What is the ball's horizontal displacement?
​

A) 84 m
B) 168 m
C) 118.8 m
D) zero
E) 237.6 ​m

Question 35

A baseball thrown from the outfield is released from shoulder height at an initial velocity of 28.1 m/s at an initial angle of 30.0° with respect to the horizontal.If it is in its trajectory for a total of 3.00 s before being caught by the third baseman at an equal shoulder-height level,what is the ball's net vertical displacement during its 3-s trajectory?
​

A) 73 m
B) 9.80 m
C) 10.1 m
D) zero
E) ​20.1 m

Question 36

A stone is thrown at an angle of 30° above the horizontal from the top edge of a cliff with an initial speed of 11.1 m/s.A stop watch measures the stone's trajectory time from top of cliff to bottom to be 5.5 s.What is the height of the cliff? (g = 9.8 m/s² and air resistance is negligible)
​

A) 179 m
B) 148 m
C) 118 m
D) 31 m
E) 137 m

Question 37

A runner circles a track of radius 150 m in 150 s moving at a constant rate.If the runner was initially moving north,what has been the runner's average acceleration when halfway around the track?
​

A) At a constant rate,the average acceleration would be zero.
B) 6.28 m/s²,west
C) 0.17 m/s²,south
D) No answer is correct.
E) ​0.17 m/s²,east

Question 38

Five boys are pushing on a snowball,and each is pushing with a force of 16.0 N.However,each boy is pushing in a different direction.They are pushing north,northeast,east,southeast,and south.(Each boy is pushing at an angle of 45.0° relative to his neighbor. )What is the magnitude of the total force on the ball?​

A) 0
B) 23 N
C) 38.6 N
D) 17.4 N
E) ​77.3 N

Question 39

A jogger runs halfway around a circular path with a radius of 50 m.What,respectively,are the magnitude of the displacement and the distance jogged?
​

A) 50 m,157 m
B) 100 m,157 m
C) 0 m,314 m
D) 100 m,314 m
E) ​50 m,314 m

Question 40

VectorIs 3.0 units in length and points along the positive x-axis;vector
Is 7.0 units in length and points along a direction 150° from the positive x-axis.What is the direction of the resultant with respect to the positive x-axis?
​

A) 49°
B) 131°
C) 41°
D) 12°
E) ​168°

Question 41

A projectile is thrown horizontally at 11.8 m/s.The projectile hits the ground 0.51 s later.What is the angle of impact the projectile makes with the horizontal ground?
​

A) -25.1°
B) -23°
C) 115.1°
D) -89.7°
E) ​-67°

Question 42

A stone is thrown at an angle of 45° above the horizontal from the top edge of a cliff with an initial speed of 15 m/s.A stop watch measures the stone's trajectory time from top of cliff to bottom to be 5.4 s.How far out from the cliff's edge does the stone travel horizontally? (g = 9.8 m/s² and air resistance is negligible)

A) 57 m
B) 81 m
C) 202 m
D) 86 m
E) 200 m

Question 43

A track star in the broad jump goes into the jump at 12 m/s and launches himself at 20° above the horizontal.How long is he in the air before returning to Earth? (g = 9.8 m/s²)
​

A) 0.42 s
B) 0.84 s
C) 1.68 s
D) 2.3 s
E) 0.89 s

Question 44

A stone is thrown with an initial speed of 10.3 m/s at an angle of 51° above the horizontal from the top of a 32 m building.If g = 9.8 m/s² and air resistance is negligible,then what is the speed of the rock as it hits the ground?
​

A) 26 m/s
B) 6 m/s
C) 27 m/s
D) 32 m/s
E) 22 m/s

Question 45

A baseball leaves the bat with a speed of 43 m/s and an angle of 45° above the horizontal.A 5.0-m-high fence is located at a horizontal distance of 136 m from the point where the ball is struck.Assuming the ball leaves the bat 1.0 m above ground level,by how much does the ball clear the fence?
​

A) 44 m
B) 32 m
C) 34 m
D) 34 m..
E) ​34 m.

Question 46

A projectile is launched at an angle θ above the horizontal.Three seconds later the projectile is moving the same angle θ below the horizontal.Which of the following (actual values with units,not just algebraic symbols)can be found from the information given?

A) the initial vertical component of the projectile's velocity
B) the initial horizontal component of the projectile's velocity
C) the initial magnitude of the velocity
D) None of the above since at least one of the above must be given to find the other two values.

Question 47

A bridge that was 6.7 m long has been washed out by the rain several days ago.How fast must a car be going to successfully jump the stream? Although the road is level on both sides of the bridge,the road on the far side is 2.3 m lower than the road on this side.
​

A) 13.8 m/s
B) 9.8 m/s
C) 8 m/s
D) 19.6 m/s
E) ​10.8 m/s

Question 48

A jet airliner moving at 530 mph due east moves into a region where the wind is blowing at 120 mph in a direction 30° north of east.What is the new velocity and direction of the aircraft?
​

A) 637 mph,5.41° N of E
B) 642 mph,5.81° N of E
C) 582 mph,8.86° N of E
D) 637 mph,10.2° N of E
E) 502 mph,9.24° N of E

Question 49

The highest mountain on Mars is Olympus Mons,rising 22 000 meters above the Martian surface.If we were to throw an object horizontally off the mountain top,how long would it take to reach the surface? (Ignore atmospheric drag forces and use g_Mars = 3.72 m/s². )

A) 1.8 minutes
B) 2.4 minutes
C) 3.0 minutes
D) 0.79 minute

Question 50

A fireman,50.4 m away from a burning building,directs a stream of water from a fire hose at an angle of 31.2° above the horizontal.If the initial speed of the stream is 46.8 m/s,at what height will the stream of water strike the building?
​

A) 42.6 m
B) 9.3 m
C) 22.8 m
D) 29.2 m
E) 27.9 m

Question 51

A rifle is aimed horizontally toward the center of a target 110 m away.If the bullet strikes 10 cm below the center,what was the velocity of the bullet? (Ignore air friction. )
​

A) 21 m/s
B) 1,089 m/s
C) 30 m/s
D) 770 m/s
E) 385 m/s

Question 52

A quarterback takes the ball from the line of scrimmage,runs backward for 11 yards,then sideways parallel to the line of scrimmage for 16 ards.He then throws a 47-yard forward pass straight downfield perpendicular to the line of scrimmage.The receiver is tackled immediately.How far is the football displaced from its original position?
​

A) 39 yards
B) 47 yards
C) 33 yards
D) 60 yards
E) 64 yards

Question 53

A ball is launched from ground level at 28 m/s at an angle of 37° above the horizontal.How far does it go before it is at ground level again?
​

A) 58 m
B) 102 m
C) 38 m
D) 77 m
E) 19 m

Question 54

A stone is thrown with an initial speed of 14.8 m/s at an angle of 51° above the horizontal from the top of a 35 m building.If g = 9.8 m/s² and air resistance is negligible,then what is the magnitude of the vertical velocity component of the rock as it hits the ground?
​

A) 24 m/s
B) 28 m/s
C) 32 m/s
D) 29 m/s
E) ​12 m/s

Question 55

A stone is thrown with an initial speed of 10.1 m/s at an angle of 58° above the horizontal from the top of a 31 m building.If g = 9.8 m/s² and air resistance is negligible,then what is the magnitude of the horizontal component of velocity as the rock strikes the ground?
​

A) 26 m/s
B) 5 m/s
C) 16 m/s
D) 5 m/s.
E) 13 m/s

Question 56

A projectile is fired directly upwards at 49 m/s.A second projectile is dropped from rest at some higher elevation at the instant the first projectile is fired and passes the first projectile 3.37 s later.From the frame of reference of the first projectile,what is the velocity of the second projectile as it passes by?
​

A) 65.5 m/s,downward
B) 73.8 m/s,downward
C) 49 m/s,downward
D) 26.4 m/s,downward
E) 109.5 m/s,downward

Question 57

A stone is thrown with an initial speed of 13.4 m/s at an angle of 53° above the horizontal from the top of a 38 m building.If g = 9.8 m/s² and air resistance is negligible,what is the magnitude of the horizontal displacement of the rock?
​

A) 33 m
B) 113 m
C) 43 m
D) 72 m
E) ​41 m

Question 58

Wiley Coyote has missed the elusive road runner once again.This time,he leaves the edge of the cliff at 50.1 m/s horizontal velocity.If the canyon is 110 m deep,how far from his starting point at the edge of the cliff does the coyote land?
​

A) 237 m
B) 168 m
C) 336 m
D) 119 m
E) ​59 m

Question 59

Superguy is flying at treetop level near Paris when he sees the Eiffel Tower elevator start to fall (the cable snapped).His x-ray vision tells him Lois LaTour is inside.If Superguy is 1.4 km away from the tower,and the elevator falls from a height of 210 m,how long does Superguy have to save Lois,and what must be his average speed?
​

A) 4.63 s,302 m/s
B) 8.02 s,175 m/s
C) 6.55 s,214 m/s
D) 9.26 s,151 m/s
E) ​3.27 s,428 m/s

Question 60

Two projectiles are launched at 100 m/s,the angle of elevation for the first being 30° and for the second 60°.Which of the following statements is false?

A) Both projectiles have the same acceleration while in flight.
B) The second projectile has the lower speed at maximum altitude.
C) Both projectiles have the same range.
D) All of the above statements are false.

Question 61

A plane is moving due north,directly towards its destination.Its airspeed is 230 mph.A constant breeze is blowing from west to east at 30 mph.In which direction is the plane pointed?
​

A) 7.4° W of N
B) 82.6° W of N
C) 44.8° W of N
D) 82.5° E of N
E) ​45.2° W of N

Question 62

A boat travels upstream and after one hour has gone 8 km.The boat next travels downstream and after one hour has gone 14 km.If the boat's speed relative to the water is constant,what is the speed of the current in the river?
​

A) 2 km/h
B) 3 km/h
C) 4 km/h
D) 5 km/h
E) ​6 km/h

Question 63

A boat moves at 12 m/s relative to the water.If the boat is in a river where the current is 2 m/s,how long does it take the boat to make a complete round trip of 1,100 m upstream followed by a 1,100-m trip downstream?

A) 220 s
B) 157.1 s
C) 188.6 s
D) 267.1 s
E) ​298.6 s

Question 64

Plane A is flying at 440 mph in the northeast direction relative to the earth.Plane B is flying at 550 mph in the north direction relative to the earth.What is the speed of Plane B as observed from Plane A?
​

A) 570 mph
B) 916 mph
C) 392 mph
D) 704 mph
E) ​714 mph

Question 65

A plane is moving due north,directly towards its destination.Its airspeed is 240 mph.A constant breeze is blowing from west to east at 20 mph.How long will it take for the plane to travel 240 miles north?
​

A) one hour
B) more than one hour
C) less than one hour
D) more information is needed
E) ​none of the above

Question 66

A plane is moving due north,directly towards its destination.Its airspeed is 240 mph.A constant breeze is blowing from west to east at 50 mph.At what rate is the plane moving north?
​

A) 235 mph
B) 245 mph
C) 230 mph
D) 225 mph
E) ​220 mph

Question 67

Plane A is flying at 350 mph in the northeast direction relative to the earth.Plane B is flying at 520 mph in the north direction relative to the earth.What is the direction of motion of Plane B as observed from Plane A?
​

A) 72.1° N of E
B) 42.2° N or W
C) 47.8° N of W
D) 17.9° N of W
E) ​41.1° N of W

Question 68

Vector 1 is 8 units long and is at 225°.Vector 2 is 5 units long and is at 120°.Vector 3 is 4 units long and is at 70°.Which vector has equal magnitude components?
​

A) Vector 3
B) Vector 1
C) Vector 2
D) None of the vectors has equal magnitude components.
E) ​Vector 2 and Vector 3

Question 69

A particle moves east at constant velocity For a time interval ΔT.It then moves north at a constant velocity,with the same speed as before,for another time interval ΔT.Finally it moves east again with the original velocity.At the instant an additional time interval ΔT has elapsed,which of the following are true about the average velocity and the average acceleration for the motion described?

A) The average velocity is and the average acceleration is zero.
B) The average velocity is and the average acceleration is not zero.
C) The average velocity is not and the average acceleration is zero.
D) The average velocity is not and the average acceleration is not zero.

Question 70

A river flows due east at 3 m/s.A boat crosses the 300-m-wide river by maintaining a constant velocity of 15 m/s due north relative to the water.If no correction is made for the current,how far downstream does the boat move by the time it reaches the far shore?
​

A) 120 m
B) 50 m
C) 45 m
D) 60 m
E) ​70 m

Question 71

Vectors,,andHave magnitudes 8,13,and 22.When these vectors are added,what is the least possible magnitude of their resultant?
​

A) 43
B) 0
C) 14
D) 1
E) ​23

Question 72

A boat moves through the water in a river at a speed of 8 m/s relative to the water.The boat makes a trip downstream and then makes a return trip upstream to the original starting place.Which trip takes longer?

A) the downstream trip
B) the upstream trip
C) Both trips take the same amount of time.
D) The answer cannot be figured without knowing the speed of the river flow.

Question 73

Four vectors all have the same magnitude.Vector 1 is at 60°,Vector 2 is at 135°,vector 3 is at 210°,and Vector 4 is at 315°.Which vector has the greatest magnitude x-component and which vector has the greatest magnitude y-component?
​

A) Vector 1,Vector 2
B) Vector 3,Vector 4
C) Vector 1,Vector 3
D) Vector 3,Vector 2
E) ​Vector 2,Vector 4

Question 74

A projectile is fired at an angle of elevation of 45°.Neglecting air resistance,what are possible angles in flight between the acceleration vector and the velocity vector?
​

A) 160° and 40°
B) 20° and 70°
C) 90° and 45°
D) none of the above
E) ​10° and 45°