Deck 3: Motion in Two and Three Dimensions

Question 1

An airplane moves at 120 m/sec to the west with respect to the air.The air moves at 50 m/sec to the south with respect to the ground.How fast does the airplane move with respect to the ground?

A)70 m/s
B)120 m/s
C)130 m/s
D)170 m/s

Answer 1

130 m/s

Question 2

A projectile is launched at 10.0 m/s in a direction 45.0 degrees above the horizon.It hits the ground 10.0 m below its initial position.What is its speed just before hitting the ground? Ignore air resistance.

A)14.1 m/s
B)17.2 m/s
C)20.0 m/s
D)24.1 m/s

Answer 2

17.2 m/s

Question 3

A skier leaves a ski jump with a horizontal velocity of 27.0 m/s (and no vertical velocity component).The skier lands 2.50 seconds later.What is the magnitude of the skier's displacement during the jump

A)98.2 m
B)74.1 m
C)30.7 m
D)67.5 m

Answer 3

74.1 m

Question 4

An object moves from a point with coordinates x = 0.0 m,y = -1.0 m,to a point with coordinates x = 8.0 m,y = -9.0 m in a time interval of 3.4 seconds.The magnitude of its the average velocity is

A)6.2 m/s.
B)5.0 m/s.
C)7.3 m/s.
D)4.9 m/s.
E)3.2 m/s

Question 5

A child kicks a football with an initial velocity of 25.0 m/s at an angle of 38 ^$\circ$ above horizontal.The ball lands at the same height from which it was kicked.What is the range of the ball?

A)24.7 m
B)39.3 m
C)51.8 m
D)61.8 m

Question 6

You are walking to catch your plane and decide to take the moving sidewalk in the airport.It has an average speed of 2.0 m/s.If you are walking with a speed of 1.5 m/s and the walkway is 85.0 m long.How long will it take you to travel the 85.0 m?

A)12 s
B)24 s
C)34 s
D)36 s
E)48 s

Question 7

A skier leaves a ski jump with a horizontal velocity (and no vertical velocity component).If the magnitude of the horizontal component of her velocity the instant before she lands is 19.6 m/s,how much time elapses between leaving the jump and landing?

A)1.0 s
B)2.7 s
C)5.4 s
D)Not enough information is given to determine the time of flight.
E)2.0 s

Question 8

A skier leaves a ski jump with a horizontal velocity (and no vertical velocity component).If the magnitude of the horizontal component of her velocity the instant before she lands two seconds later is 15.0 m/s,what was the horizontal component of her initial velocity

A)24.0 m/s.
B)19.6 m/s.
C)15.0 m/s.
D)43.6 m/s.
E)0 m/s.

Question 9

A skier leaves a ski jump with a horizontal velocity of 21.0 m/s (and no vertical velocity component).The skier lands three seconds later.What is the magnitude of the horizontal component of the skier's displacement during the jump

A)32.2 m
B)63.0 m
C)44.1 m
D)51.8 m

Question 10

If the launch speed of a kicked football was doubled,then by what factor would its hang time increase?

A)the square root of two
B)two
C)four
D)eight

Question 11

The maximum height above ground you can achieve with a projectile launched vertically upward from ground level,if you are able to give it an initial speed of 65.0 m/s,is

A)336 m.
B)215 m.
C)125 m.
D)6.36 m.

Question 12

A projectile is launched at a speed 10.0 m/s at angle of 20.0 ^$\circ$ above horizontal.What is the magnitude of its acceleration at maximum height?

A)0.0 m/s²
B)9.40 m/s²
C)9.81 m/s²
D)19.8 m/s²

Question 13

You toss a stone vertically upward and it reaches a maximum height of 2.06 m above the launch point.The initial velocity of the stone was

A)336 m.
B)215 m.
C)125 m.
D)6.36 m.

Question 14

An arrow is shot at ground level with an initial speed of 50.0 m/s at an angle of 25.0 ^$\circ$ above horizontal.What is its x-coordinate when the arrow is on the way up and its y coordinate is 5.00 m above the ground?

A)5.44 m
B)11.4 m
C)84.3 m
D)184 m
E)203 m

Question 15

An airplane's speed with respect to the air is 100 m/sec.The velocity of the air with respect to the ground is 30.0 m/sec to the northeast.What is the direction of the airplane's velocity with respect to the air if the direction of its velocity with respect to the ground is due east?

A)3.00 degrees south of east
B)4.50 degrees south of east
C)12.2 degrees south of east
D)17.5 degrees south of east

Question 16

A skier leaves a ski jump with a horizontal velocity (and no vertical velocity component).If the magnitude of the vertical component of her velocity the instant before she lands is 25 m/s,how much time elapses between leaving the jump and landing?

A)2.0 s
B)1.0 s
C)4.6 s
D)2.5 s
E)Not enough information is given to determine the time of flight.

Question 17

A skier leaves a ski jump with a horizontal velocity of 24.0 m/s (and no vertical velocity component).The skier lands two seconds later.What is the magnitude of the vertical component of the skier's displacement during the jump

A)32.2 m
B)19.6 m
C)48.0 m
D)28.3 m

Question 18

A skier leaves a ski jump with a horizontal velocity of 24.0 m/s (and no vertical velocity component).The magnitude of the vertical component of her velocity the instant before she lands two seconds later is

A)24.0 m/s.
B)0 m/s.
C)43.6 m/s.
D)19.6 m/s.

Question 19

A bullet is shot horizontally from the edge of a cliff at a height of 100 m above the ground.The initial speed of the bullet is 150 m/s.It hits the ground from the base of the cliff at a horizontal distance of

A)158 m.
B)278 m.
C)498 m.
D)677 m.
E)868 m

Question 20

At what angle measured with the horizon must a projectile be launched such that its range is equal to its maximum height? Ignore air resistance.

A)45.0 degrees
B)60.0 degrees
C)63.2 degrees
D)76.0 degrees

Question 21

Two boats leave the port at the same time.Boat A has a velocity of (4î - 3ĵ)m/s and boat B has a velocity of (3î + 4ĵ)m/s as measured by someone standing at the port ( and are unit vectors along the x-axis and the y-axis respectively).What is the position vector of boat A as seen by a person travelling on boat B after 100 seconds has elapsed? Give your answer as magnitude and direction.

A)707.1 m and 81.87º
B)707.1 m and 261.87º
C)424.3 m and 188.13º
D)126.7 m and 88.26º
E)989.9 m and 312.87 ^$\circ$

Question 22

As the Earth travels around the Sun the Moon is traveling around the Earth.Find the maximum speed of the Moon (relative to the Sun)as it travels around the Sun.The Earth's orbital radius around the Sun is 1.50 * 10¹¹ m and the Moon's orbit has a radius of 3.85 * 10⁸ m.The time for the Earth's journey around the Sun is 3.156 * 10⁷ s and the Moon takes 2.36 * 10⁶ s to travel around the Earth.

A)32600 m/s
B)28800 m/s
C)4515 m/s
D)30900 m/s

Question 23

A battleship shoots a projectile A at a target at an angle of 30 ^$\circ$ with respect to the horizontal.Simultaneously,it shoots a projectile B at the same target at an angle of 60 ^$\circ$ with respect to the horizontal.Which projectile hits the target first?

A)projectile A
B)projectile B
C)They both hit at the same time.
D)Only one projectile hits the target.
E)More information is needed.

Question 24

A human cannonball is launched from a height of 2.0 m at an angle of 55 degrees with respect to horizontal and an initial speed of 18 m/s.How much time elapses before the human cannon ball lands in the net,which is also 2.0 m above the ground?

A)1.83 s
B)1.51 s
C)3.14 s
D)3.01 s
E)3.67 s

Question 25

The x and y positions (in meters)of a particle are given by: x(t)= 253 t,and y(t)= -12.0 t² + 155 t + 100.The magnitude of the particle's acceleration at t = 12.9 s is

A)0 m/s².
B)-12.0 m/s².
C)12.0 m/s².
D)-24.0 m/s².
E)24.0 m/s².

Question 26

A soccer player kicks a ball,giving it an initial velocity of 17.2 m/s in the horizontal direction and 12.0 m/s in the vertical direction.How far down the field does the ball travel before landing?

A)84.2 m
B)42.1 m
C)81.6 m
D)24.0 m
E)37.5 m

Question 27

What is the range of a football punted with an initial velocity of 24 m/s kicked at an angle of 51 ^$\circ$ above the horizontal? The ball leaves the punter's foot at an initial height of 1.1 m and is allowed to hit the ground.

A)35.5 m
B)57.5 m
C)58.3 m
D)61.8 m

Question 28

A cannon shell is shot horizontally from the top of a 50-m tall cliff at a speed of 5 m/s and an angle of 30 ^$\circ$ above the horizontal.How far from the base of the cliff does the cannon shell hit the ground?

A)11.2 m
B)12.4 m
C)30.1 m
D)7.63 m
E)15.0 m

Question 29

As the Earth travels around the Sun the Moon is traveling around the Earth.Find the minimum speed of the Moon (relative to the Sun)as it travels around the Sun.The Earth's orbital radius around the Sun is 1.50 * 10¹¹ m and the Moon's orbit has a radius of 3.85 * 10⁸ m.The time for the Earth's journey around the Sun is 3.156 * 10⁷ s and the Moon takes 2.36 * 10⁶ s to travel around the Earth.

A)-4590 m/s (The negative sign indicates it travels backwards compared to the Earth's orbit.)
B)4590 m/s
C)22600 m/s
D)28800 m/s

Question 30

A movie stunt woman takes a running jump from the roof of one building to that of a lower building.She leaves the taller building traveling perfectly horizontally at 6.1 m/s and just makes it to the edge of the roof of the lower building.The horizontal gap between the buildings is 2.8 m.The difference in height between the two buildings is

A)1.0 m.
B)1.4 m.
C)2.3 m.
D)2.8 m.
E)3.0 m.

Question 31

In 1971,Alan Shepard hit two golf-balls on the surface of the Moon (where the acceleration due to gravity is only 1.62 m/s²).If the launch angle was 27 ^$\circ$ and the ball traveled 400 m,what was the initial speed of the ball?

A)28 m/s
B)38 m/s
C)70 m/s
D)801 m/s

Question 32

A golf ball is hit and makes a 45 ^$\circ$ angle with the horizontal as it leaves the tee.It lands 200 m away.What was the ball's initial speed?

A)35.11 m/s
B)26.82 m/s
C)44.27 m/s
D)56.82 m/s
E)31.44 m/s

Question 33

A golf ball is hit horizontally from the edge of a ramp.It lands at an elevation 200 m below and its trajectory upon landing is 45 ^$\circ$ angle below the horizontal.What was the ball's initial speed?

A)34.7 m/s
B)27.5 m/s
C)51.8 m/s
D)62.6 m/s
E)45.3 m/s

Question 34

An object is launched up a 30 degree slope at an angle of 20 degrees above the incline of the slope and lands a distance of 3.12 m up the slope.What is the object's initial speed?

A)5.94 m/s
B)5.00 m/s
C)6.89 m/s
D)5.23 m/s
E)7.23 m/s

Question 35

Tennis ball A is dropped from a height of 15 m.Tennis ball B is thrown horizontally from a height of 15 m with a horizontal velocity of 25 m/s.Which tennis ball hits the ground first?

A)ball A
B)ball B
C)They both hit at the same time.
D)Neither ball hits the ground.
E)More information is needed.

Question 36

Two boats leave the port at the same time.Boat A has a velocity of m/s and boat B has a velocity of m/s as measured by someone standing at the port ( and are unit vectors along the x-axis and the y-axis respectively).What is the position vector of boat B as seen by a person travelling on boat A after 60 seconds has elapsed? Give your answer as magnitude and direction.

A)424.3 m and 88.26º
B)424.3 m and 188.13º
C)126.7 m and 188.13º
D)126.7 m and 88.26º
E)300.0 m and 36.87 ^$\circ$

Question 37

An object is launched up a 30 degree slope at an angle of 20 degrees above the incline of the slope with an initial speed of 5.0 m/s.How far up the slope does the object land?

A)1.49 m
B)2.36 m
C)3.82 m
D)4.98 m
E)2.50 m

Question 38

The x and y positions (in meters)of a particle are given by: x(t)= 253 t,and y(t)= -12.0 t² + 155 t + 100.The speed of the particle at t = 12.9 s is

A)0 m/s.
B)98.4 m/s.
C)296 m/s.
D)408 m/s.
E)529 m/s.

Question 39

What is the maximum height of a projectile shot at an angle of 25 ^$\circ$ with respect to the horizontal and initial speed of 22 m/s?

A)8.86 m
B)4.41 m
C)20.28 m
D)10.14 m
E)None are correct.More information is needed.

Question 40

The shot "heard 'round the world" was fired in Concord at the beginning of the American Revolution.The muskets of the day had minimal sights and often were aimed by merely looking down the barrel.If the bullet was fired horizontally with an initial speed of 250 m/s,how far did the bullet drop by the time it hit the British line,75 m away?

A)0 m (the bullet traveled in a horizontal line)
B)0.44 m
C)1.47 m
D)7.65 m

Question 41

Bill is riding a flatbed railroad car travelling down the tracks at 16 m/s.The instant he passes Ted on the side of the train tracks,he throws a water balloon at him at such an angle that the balloon travels perpendicular to the train's direction of motion and strikes Ted squarely in the face.If Bill threw the balloon relative to the train at a speed of 24 m/s,with what speed did the balloon hit his friend?

A)8 m/s
B)18 m/s
C)24 m/s
D)29 m/s

Question 42

A plane,diving at an angle of 37 ^$\circ$ below the horizontal,releases a projectile at an altitude of 730.0 m.The projectile hits the ground 5.00 s after being released.At what angle does the projectile strike the ground?

A)45.0 ^$\circ$ below the horizontal
B)43.4 ^$\circ$ below the horizontal
C)53.0 ^$\circ$ below the horizontal
D)37.0 ^$\circ$ below the horizontal
E)44.1 ^$\circ$ below the horizontal

Question 43

The position of a particle as a function of time is given by. Its velocity at t = 3 s is

A)5 -21
.
B)27 -54.

C)34 -61.

D)21 -7

Question 44

A boat crosses a stream which is flowing at 10.0 m/s.The driver of the boat wants to cross the river and arrive directly across the river from where he departed (point A to point B).What boat speed in m/s is needed to go directly across the river if the driver steers upstream with $\theta$ = 30.0 ^$\circ$ as shown?

A)7.5
B)10.0
C)15.0
D)20.0
E)25.0

Question 45

A boat crosses a river which is flowing at 10.0 m/s.The driver of the boat wants to cross the river and arrive directly across the river from where he departed (point A to point B).If the speed of the boat relative to the river is 15.0 m/s,what angle, $\theta$ must the driver steer the boat?

A)41.8 ^$\circ$
B)48.2 ^$\circ$
C)70.5 ^$\circ$
D)36.7 ^$\circ$
E)33.7 ^$\circ$

Question 46

A gun is fired horizontally from the top of a cliff with a velocity of 325 m/s.How far does the bullet drop in meters below the horizontal in 1.2 seconds?

A)325
B)19.8
C)124
D)1329
E)7.1

Question 47

The wind is blowing due west with a speed of 16 m/s,and a pilot with a 30 m/s plane wants to fly due north.Which picture below best describes what the heading of the plane should be?

A)a
B)b
C)c
D)d
E)e

Question 48

A ball is thrown from the ground.Its velocity after 4 seconds is (15 -3 )m/s.the range of the ball is

A)205 m.
B)189 m.
C)111 m.
D)98 m.

Question 49

A particle moves from an initial position with coordinates x = +7.0 m,y = +2.0 m,to an intermediate position with coordinates x = +4.0 m,y = +5.0 m in a time interval of 3.0 s.The particle then moves from the intermediate position with coordinates x = +4.0 m,y = +5.0 m,to a final position with coordinates x = +1.0 m,y = +8.0 m in a time interval of 6 s.What is the magnitude of the average velocity for the total displacement?

A)0.94 m/s
B)1.1 m/s
C)1.3 m/s
D)2.1 m/s
E)3.0 m/s

Question 50

A golf ball is hit with an initial angle of 32.3 ^$\circ$ with respect to the horizontal and an initial velocity of 89.7 mph.It lands a distance of 96.2 m away from where it was hit.By how much (in meters)did the wind resistance reduce the range of the golf ball?

A)17.0
B)24.6
C)35.7
D)51.8
E)75.1

Question 51

A ball is launched from horizontal ground from the origin with an initial speed v_o and angle 45 ^$\circ$ above the horizontal.What is the horizontal position of the projectile when its horizontal position is equal to twice its vertical position?

A)v_o²/g
B)v_o²/2g
C)3v_o²/2g
D)2v_o²/g

Question 52

A football resting on the ground is kicked at an angle of 35.0 ^$\circ$ towards the uprights with an initial speed of 20.0 m/s.What is the maximum height (in meters)reached by the ball?

A)1.75
B)6.71
C)3.12
D)0.12
E)9.24

Question 53

A tube is mounted on a railcar which is moving at 30 m/s.Rain is falling vertically at a constant rate of 12 m/s.The minimum angle of tilt of the tube for not getting any rain on its inside is

A)45.1 ^$\circ$ .
B)28.5 ^$\circ$ .
C)21.8 ^$\circ$ .
D)18.4 ^$\circ$ .

Question 54

Bill is riding a flatbed railroad car travelling down the tracks at 16 m/s.The instant he passes Ted on the side of the train tracks,he throws a water balloon at him.At what angle relative to the train's direction of motion must Bill throw the balloon in order to hit Ted squarely in the face,assuming he can throw an object with a speed of 24 m/s?

A)42 ^$\circ$
B)48 ^$\circ$
C)90 ^$\circ$
D)132 ^$\circ$
E)138 ^$\circ$

Question 55

A boat crosses a river which is flowing at 6.0 m/s.The boat travels directly across the river from A to B and the speed of the boat relative to the river is 8.0 m/s.If the width of the river is 80.0 m,how long does it take the boat to cross the river?

A)10.0 s
B)13.3 s
C)5.71 s
D)15.1 s
E)40.0 s

Question 56

A particle moves from an initial position with coordinates x = -2.0 m,y = +3.0 m,to a final position with coordinates x = +5.0 m,y = +7.0 m in a time interval of 10 s.What is the magnitude of the average velocity for this displacement?

A)0.30 m/s
B)0.50 m/s
C)0.54 m/s
D)0.81 m/s
E)1.1 m/s

Question 57

In a cathode ray tube electrons are initially travelling horizontally at 4 *10⁶ m/s.The horizontal distance electrons would have to travel for a vertical drop of 0.2 mm in vacuum is

A)400 m.
B)1500 m.
C)3.8 km.
D)25.5 km.

Question 58

A machine can toss a golf ball a distance of 120 m on a level field when the machine is set to an angle of 30 degrees.How far can the machine toss a golf ball when it is set to an angle of 45 degrees?

A)85 m
B)98 m
C)140 m
D)150 m
E)170 m

Question 59

I throw a ball into the air at some angle with respect to the horizontal.Neglecting the effect of friction,which of the following statements about the ball is true?

A)The acceleration is zero at the top of the motion.
B)The velocity is zero at the top of the motion.
C)The velocity is constant during the motion.
D)The vertical component of the velocity is constant during the motion.
E)The vertical component of the velocity is zero at the top.

Question 60

A ball is thrown from the ground.Its velocity after 4 seconds is (15 -3 )m/s.The hang time of the ball is

A)7.4 s.
B)9.8 s.
C)11.9 s.
D)17.8 s.

Question 61

A boat crosses a river which is flowing at 6.0 m/s.The boat travels directly across the river from A to B and the speed of the boat relative to the river is 10.0 m/s.While it is crossing the river,what is the speed of the boat relative to the shore (point a)

A)4.0 m/s
B)12.4 m/s
C)11.7 m/s
D)16.0 m/s
E)8.0 m/s

Question 62

A ball is thrown up in the air with a velocity v at an angle 45 ^$\circ$ with respect to the ground.At the very top of its motion the y-component of the acceleration will be

A)zero.
B)-g
C)g.
D)g/2.
E)-g/2.

Question 63

A rock is thrown horizontally from a bridge 55 m high with a velocity of 8 m/s.How far does the rock travel horizontally before hitting the water?

A)24.7 m
B)26.8 m
C)28.9 m
D)31.0 m
E)33.1 m

Question 64

Bullet A is dropped,from rest,at the same time that another bullet B is fired horizontally from a rifle.If both bullets leave from the same height above ground,then

A)Bullet A hits the ground before bullet B.
B)both bullets hit the ground at the same time.
C)Bullet B hits the ground before bullet A.

Question 65

A ball is thrown horizontally from a 63.0 m high building with a speed of 32.0 m/s.What is the vertical component of the velocity when it hits the ground?

A)35.2 m/s
B)47.5 m/s
C)32.0 m/s
D)65.0 m/s
E)24.8 m/s

Question 66

A boat crosses a river which is flowing at 6.0 m/s.The boat travels directly across the river from A to B and the speed of the boat relative to the river is 9.0 m/s.If it takes the boat 10.0 seconds to cross the river,how wide is the river?

A)108.1 m
B)89.2 m
C)67.1 m
D)60.0 m
E)150.0 m

Question 67

A ball is thrown horizontally from a 48.0 m high building with a speed of 28.0 m/s.What is the magnitude of the velocity when it hits the ground?

A)52.9 m/s
B)41.5 m/s
C)58.7 m/s
D)48.1 m/s
E)68.1 m/s

Question 68

A baseball is hit at a 45 ^$\circ$ angle with a speed of 50 meters/second.How far does it go (in meters)before it hits the ground (within 5% accuracy)? (Ignore wind resistance and assume that the ground level is the same as the level it was hit from.)

A)125 m
B)250 m
C)500 m
D)1000 m
E)2000 m

Question 69

A ball is thrown horizontally from a 49 m high building with a speed of 23 m/s.What is the horizontal component of the velocity when it hits the ground?

A)49 m/s
B)23 m/s
C)11.5 m/s
D)3.3 m/s
E)0

Question 70

A plane flying at a speed 180 mph over the ocean drops an 81 kg package straight down.A boat 3 miles below is sent to intercept the package.How far away does the boat have to travel from the drop point to retrieve the package? (1mile=1.609 km)

A)0 km
B)0.08 km
C)0.29 km
D)1.4 km
E)2.5 km

Question 71

A ball is thrown upward with a velocity of 17.0 m/s at an angle of 50.0 ^$\circ$ with respect to the horizontal.What will be its speed in m/s after 0.800 seconds?

A)6.5
B)19.8
C)17.0
D)-5.4
E)12.1

Question 72

A ball is thrown horizontally from a 58.0 m high building with a speed of 36.0 m/s.What is the direction of the ball's velocity,relative to the horizontal when it hits the ground?

A)-49.0^o
B)-55.8^o
C)-45.0^o
D)-43.1^o
E)-46.9^o

Question 73

A roller coaster in an amusement park first goes up an incline of length 70 m and at an angle of 38 ^$\circ$ to the horizontal.It then goes straight along the horizontal for 20 m.It finally goes down a 30 m long ramp with an angle of 60 ^$\circ$ relative to the horizontal.What is the displacement of the roller coaster at that point relative to its starting point? (Hint: Notation: (x,y);It really helps to make a drawing here.)

A)(90 m,17 m)
B)(120 m,0 m)
C)(120 m,17 m)
D)(90 m,0 m)
E)(120m,69m)