Deck 3: Motion in Two Dimensions

Question 1

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

Answer 1

at the top of the trajectory

Question 2

In a two-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

Answer 2

cosine

Question 3

​A startled deer runs 520 m at 20.0° north of east for half a minute,then turns and runs 380 m at 55.0° north of west for 15.0 seconds and stops.What is the average velocity of the deer during this time?

A)​14.3 m/s
B)​12.4 m/s
C)​20.0 m/s
D)​36.1 m/s

Answer 3

​12.4 m/s

Question 4

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 5

A mouse starts out in a corner of a room,and runs across the floor according to the following displacements:
D_​1: 1.2 m
+ 0)4 m
D​₂: 0.2 m
- 0)8 m
What is the magnitude of the total displacement of the mouse's position?

A)​1.5 m
B)​2.6 m
C)​1.0 m
D)​1.8 m

Question 6

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 7

In a two-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

Question 8

A car is initially traveling west at 25 mph,and makes a turn north.As the car finishes the turn,its velocity is 20 mph north.It takes 3.5 seconds to complete the turn.What is the average acceleration of the car while it is turning,in mph/s?​ Let east be the positive-x direction and north be the positive-y direction.

A)​-7.1 + 5.7
B)​7.1 - 5.7
C)​5.7 - 7.1
D)​-5.7 + 7.1

Question 9

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

Question 10

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 11

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 12

John throws a baseball from the outfield from shoulder height,at an initial velocity of 41.5 m/s at an initial angle of 40.0° with respect to the horizontal.The ball is in its trajectory for a total interval of 5.00 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)159 m
B)267 m
C)174 m
D)zero
E)495 ​m

Question 13

In a two-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 14

An object moves at a constant velocity of 12 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 24 m/s.
B)12 m/s
C)6 m/s
D)More information is needed.
E)​24 m/s

Question 15

A helicopter is traveling at 50.0 m/s at a constant altitude of 150 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)63 m/s
B)55 m/s
C)74 m/s
D)​54 m/s

Question 16

A jogger runs halfway around a circular path with a radius of 60.0 m.What,respectively,are the magnitude of the displacement and the distance jogged?

A)60.0 m,188 m
B)120 m,188 m
C)0 m,377 m
D)120 m,377 m
E)​60.0 m,377 m

Question 17

A string attached to an airborne kite is maintained at an angle of 44.0° with the horizontal.If a total of 160 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)111 m
B)80.0 m
C)31.7 m
D)115 m
E)155 m

Question 18

A baseball thrown from the outfield is released from shoulder height at an initial velocity of 28.3 m/s at an initial angle of 30.0° with respect to the horizontal.If it is in its trajectory for a total of 4.00 s before being caught by the third baseman at an equal shoulder-height level,what is the ball's net vertical displacement during its 4.00-s trajectory?​

A)98.0 m
B)9.80 m
C)10.2 m
D)zero
E)​20.4 m

Question 19

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 30.0° with respect to the horizontal.What is the maximum vertical displacement that the ball reaches during its trajectory?​

A)10.8 m
B)21.6 m
C)32.4 m
D)14.4 m
E)28.8 m

Question 20

A car's initial velocity is 50.0 km/h in the direction 60.0° north of east,and its final velocity is 70.0 km/h in the direction 40.0° south of east.If the time period for this journey is 30.0 minutes,what is the magnitude of the car's average acceleration?​

A)186​ km/h/h
B)​240 km/h/h
C)​92.8 km/h/h
D)​3.94 km/h/h

Question 21

A ball is rolled horizontally off a table with an initial speed of 0.24 m/s.A stopwatch measures the ball's trajectory time from table to the floor to be 0.36 s.What is the height of the table? (g = 9.8 m/s² and air resistance is negligible)

A)0.72 m
B)0.55 m
C)0.016 m
D)0.64 m
E)0.65 m

Question 22

A projectile is launched with speed v at an angle θ,the angle being less than 45º.What other angle would give the same range for this projectile launched at the same speed v?

A)2θ
B)0.5θ
C)90° - θ
D)90º - 0.5θ

Question 23

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 24

A stone is thrown at an angle of 30° above the horizontal from the top edge of a cliff with an initial speed of 8.0 m/s.A stop watch measures the stone's trajectory time from top of cliff to bottom to be 5.9 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)41 m
B)27 m
C)300 m
D)130 m

Question 25

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 1.00 km away from the tower,and the elevator falls from a height of 230 m,how long does Superguy have to save Lois,and what must be his average speed?​

A)4.84 s,206 m/s
B)8.39 s,119 m/s
C)6.85 s,150 m/s
D)9.69 s,103 m/s
E)​3.43 s,292 m/s

Question 26

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 27

A ball is launched from ground level at 25 m/s at an angle of 31° above the horizontal.How far does it go before it is at ground level again?

A)34 m
B)94 m
C)28 m
D)56 m
E)14 m

Question 28

A baseball leaves the bat with a speed of 47 m/s and an angle of 45° above the horizontal.A 5.0-m-high fence is located at a horizontal distance of 137 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)59.7 m
B)47.7 m
C)49.7 m
D)121 m

Question 29

A projectile is fired at an angle of elevation of 30°.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 30°
D)none of the above
E)10° and 30°

Question 30

Wiley Coyote has missed the elusive road runner once again.This time,he leaves the edge of the cliff at 52.4 m/s horizontal velocity.If the canyon is 140 m deep,how far from his starting point at the edge of the cliff does the coyote land?

A)280 m
B)198 m
C)396 m
D)140 m
E)70.0 m

Question 31

A bridge that was 10.4 m long has been washed out by the rain several days ago.How fast must a car be going to successfully jump the stream,if we neglect air resistance? Although the road is level on both sides of the bridge,the road on the far side is 3.00 m lower than the road on this side.

A)18.8 m/s
B)13.3 m/s
C)10.9 m/s
D)26.6 m/s
E)14.3 m/s

Question 32

A projectile is thrown horizontally at 11.5 m/s.The projectile hits the ground 0.570 s later.What is the angle of impact the projectile makes with the horizontal ground?

A)-29.1°
B)-25.9°
C)119°
D)-89.7°
E)-64.1°

Question 33

Two baseballs are released at the same time.One is dropped from rest and the other is given an initial horizontal velocity.Which of the following is not true? Ignore atmospheric drag.

A)Both baseballs hit the ground at the same time.
B)Both have the same vertical component of velocity as they reach impact.
C)The horizontal component of velocity increases at a greater rate than the vertical component of velocity for both while they are both in the air.
D)The horizontally-released ball has a greater speed than the other ball for the whole trip.

Question 34

A rifle is aimed horizontally toward the center of a target 120 m away.If the bullet strikes 11.2 cm below the center,what was the velocity of the bullet? (Ignore air friction. )

A)23 m/s
B)1 120 m/s
C)32 m/s
D)790 m/s
E)400 m/s

Question 35

A ball is rolled horizontally off a table with an initial speed of 0.24 m/s.A stop watch measures the ball's trajectory time from table to the floor to be 0.20 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)0.048 m
C)0.39 m
D)0.15 m
E)0.47 m

Question 36

A fireman,57.6 m away from a burning building,directs a stream of water from a fire hose at an angle of 35.2° above the horizontal.If the initial speed of the stream is 42.7 m/s,at what height will the stream of water strike the building?​

A)44.2 m
B)13.8 m
C)27.3 m
D)30.8 m
E)36.4 m

Question 37

A track star in the broad jump goes into the jump at 12.0 m/s and launches himself at 26.0° above the horizontal.How long is he in the air before returning to Earth? (g = 9.8 m/s²)

A)0.5 s
B)1.1 s
C)2.1 s
D)2.2 s
E)1.2 s

Question 38

A stone is thrown at an angle of 30° above the horizontal from the top edge of a cliff with an initial speed of 12 m/s.A stop watch measures the stone's trajectory time from top of cliff to bottom to be 4.8 s.What is the height of the cliff? (g = 9.8 m/s² and air resistance is negligible)

A)140 m
B)110 m
C)84 m
D)29 m

Question 39

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 true.

Question 40

A quarterback takes the ball from the line of scrimmage,runs backward for 12 yards,then sideways parallel to the line of scrimmage for 18 yards.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)31 yards
D)62 yards
E)66 yards

Question 41

Plane A is flying at 350 mph in the northeast direction relative to the Earth.Plane B is flying at 460 mph in the north direction relative to the Earth.What is the direction of motion of Plane B as observed from Plane A?

A)70.7° N of E
B)49.3° N of W
C)40.7° N of W
D)19.3° N of W
E)48.2° N of E

Question 42

A projectile is fired directly upwards at 49.4 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 3.00 s later.From the frame of reference of the first projectile,what is the velocity of the second projectile as it passes by?

A)64.1 m/s,downward
B)71.5 m/s,downward
C)49.4 m/s,downward
D)34.7 m/s,downward
E)104 m/s,downward

Question 43

A stone is thrown with an initial speed of 11.5 m/s at an angle of 50.0 above the horizontal from the top of a 30.0-m-tall building. Assume air resistance is negligible, and g = 9.8 m/s2.
What is the speed of the rock as it hits the ground?

A)11.5 m/s
B)26.8 m/s
C)24.5 m/s
D)16.2 m/s

Question 44

A boat travels upstream and after one hour has gone 10 km.The boat next travels downstream and after one hour has gone 18 km.If the boat's speed relative to the water is constant,what is the speed of the current in the river?

A)3 km/h
B)4 km/h
C)5 km/h
D)6 km/h
E)7 km/h

Question 45

A plane is moving due north,directly towards its destination.Its airspeed is 210 mph.A constant breeze is blowing from west to east at 25.0 mph.In which direction is the plane pointed?

A)6.79° W of N
B)83.2° W of N
C)44.8° W of N
D)83.2° E of N
E)45.2° E of N

Question 46

A stone is thrown with an initial speed of 11.5 m/s at an angle of 50.0 above the horizontal from the top of a 30.0-m-tall building. Assume air resistance is negligible, and g = 9.8 m/s2.
What is the magnitude of the horizontal displacement of the rock?

A)3.53 m
B)13.3 m
C)222 m
D)26.1 m

Question 47

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 48

A jet airliner moving at 470 mph due east moves into a region where the wind is blowing at 110 mph in a direction 30.0° north of east.What is the new velocity and direction of the aircraft?

A)568 mph,5.56° N of E
B)573 mph,5.98° N of E
C)520 mph,9.06° N of E
D)568 mph,10.4° N of E
E)448 mph,9.45° N of E

Question 49

A projectile is launched at an angle less than 30° and at speed v.Which will increase the projectile's range more,ignoring atmospheric drag?

A)doubling the launch angle
B)increasing the speed of launch by 50%
C)reducing the mass of the projectile
D)launching on February 29th

Question 50

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 51

A boat moves at 10.8 m/s relative to the water.If the boat is in a river where the current is 2.00 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)250 s
B)172 s
C)211 s
D)297 s
E)​336 s

Question 52

A plane is moving due north,directly towards its destination.Its airspeed is 220 mph.A constant breeze is blowing from west to east at 50 mph.How long will it take for the plane to travel 220 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 53

A stone is thrown with an initial speed of 11.5 m/s at an angle of 50.0 above the horizontal from the top of a 30.0-m-tall building. Assume air resistance is negligible, and g = 9.8 m/s2.
What is the magnitude of the horizontal-velocity component of the rock as it hits the ground?

A)79.5 m/s
B)8.81 m/s
C)58.7 m/s
D)7.39 m/s

Question 54

A plane is moving due north,directly towards its destination.Its airspeed is 210 mph.A constant breeze is blowing from west to east at 20.0 mph.At what rate is the plane moving north?

A)209 mph
B)211 mph
C)204 mph
D)199 mph
E)194 mph

Question 55

A river flows due east at 2.0 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)80 m
B)30 m
C)25 m
D)40 m
E)​50 m

Question 56

A stone is thrown with an initial speed of 11.5 m/s at an angle of 50.0 above the horizontal from the top of a 30.0-m-tall building. Assume air resistance is negligible, and g = 9.8 m/s2.
What is the magnitude of the vertical-velocity component of the rock as it hits the ground?

A)8.81 m/s
B)7.39 m/s
C)25.8 m/s
D)19.3 m/s