Student Worksheets

Unit 2 - Kinematics (Two-Dimensional)

From The Physics Classroom’s Physics Interactives http://www.physicsclassroom.com!

©The Physics Classroom, All Rights Reserved This document should NOT appear on other websites.

Horizontally-Launched Projectiles Goal: To understand the conceptual nature of the motion of a horizontally-launched projectile. Background: A projectile is an object that is projected or launched into the air and then moves through the air under the sole influence of gravity. In this sense, a projectile is a free-falling object that experiences a downward acceleration of approximately 10 m/s/s. Getting Ready: Navigate to the Projectile Simulator in the Physics Interactives section of The Physics Classroom website:

http://www.physicsclassroom.com/Physics-Interactives/Vectors-and-Projectiles/Projectile-Simulator

Path: physicsclassroom.com => Physics Interactives => Vectors and Projectiles => Projectile Launcher

Once the Interactive opens, resize it to whatever size you wish. Then set the Speed to 10 m/s. Set the Angle to 0 degrees. Set the Height to 120 m. Select Show Velocity Vectors in order to enable this feature. Directions and Questions:

1. Click the Start button and observe the simulation. The red arrows are velocity vectors. They are indicators of how fast the object is moving horizontally and vertically. The length of the arrow indicates how fast the object is moving in that direction. Does the object change how fast it is moving in the horizontal direction? _________

Explain why you answered this way. 2. Reset and Start the animation again to answer the following question: Does the object change

how fast it is moving in the vertical direction? _________ Explain why you answered this way. 3. How does the initial horizontal velocity (right after it starts moving) compare to the final

horizontal velocity (just before hitting the ground)? a. They are equal. b. The initial is greater c. The final is greater 4. How does the initial vertical velocity (right after it starts moving) compare to the final vertical

velocity (just before hitting the ground)? a. They are equal. b. The initial is greater c. The final is greater 5. Acceleration involves a change in speed. In which direction does a projectile accelerate? a. Horizontally only b. Vertically only c. Both horizontally and vertically d. Neither horizontally and vertically

1

From The Physics Classroom’s Physics Interactives http://www.physicsclassroom.com!

©The Physics Classroom, All Rights Reserved This document should NOT appear on other websites.

6. Now run the several trials to fill in the table. Click Reset after each trial to prepare for the next.

Keep the initial height at 120 m and the angle at 0 degrees.

Trial Speed (m/s) Time (s) x-Displacement (m) 1 10

2 20

3 30

4 40

5 60 Analyze the data above to answer the following questions.

7. Describe the effect that increasing launch speed has upon the time to fall. 8. Describe the effect that increasing launch speed has upon the horizontal or x-displacement. 9. A doubling of launch speed causes the time to fall to _____ and the x-displacement to _____. a. double, double b. halve, double c. not change, double d. double, not change e. double, halve f. not change, halve 10. Which two trials could be used to show the effect that a tripling of the launch speed has upon the

time and x-displacement? a. Trials 1 and 2 b. Trials 2 and 4 c. Trials 2 and 5 11. Experiment with the Interactive in order to determine what changes must be made in order to

decrease the time to fall. Describe what you changed, what you observed, and what you conclude:

What I changed: What I observed: What I conclude regarding what changes must be made to decrease the time to fall:

2

Worksheet: Projectile Problems Name___________________

PHYSICSFundamentals © 2004, GPB

4-16

To solve projectile problems, you must divide up your information into two parts:

___________________ which has _________________ motion and

____________________ which has __________________ motion. What

equations will you use for each type of motion?

1. A ball rolls off a 1.0 m high table and lands on the floor, 3.0 m away from the

table.

a. How long is the ball in the air?

b. With what horizontal velocity did the ball roll off the table?

c. What is the vertical velocity of the ball just before it hits the floor?

d. What is the horizontal velocity of the ball just before it hits the floor?

2. A carpenter tosses a shingle off a 9.4 m high roof, giving it an initial horizontal

velocity of 7.2 m/s.

(a) What is the final vertical velocity of the ball?

(b) How long does it take to reach the ground?

(c) How far does it move horizontally in this time?

3

(Ans.45 sec)(Ans. 6.7 m/s)

(Ans.-4.41 m/s)(Ans. 6.7 m/s)

(Ans. -13.7 m/s)(Ans. 1.4 s)

(Ans. 10.1 m)

Worksheet: Projectile Problems Name___________________

PHYSICSFundamentals © 2004, GPB

4-17

3. A tiger leaps horizontally from a 12 m high rock with a speed of 4.5 m/s. How

far from the base of the rock will she land?

4. A diver running 1.6 m/s dives out horizontally from the edge of a vertical cliff

and reaches the water 3.0 s later. How high was the cliff and how far from its

base did the diver hit the water?

5. You toss an apple horizontally at 9.5 m/s from a height of 1.8 m.

Simultaneously, you drop a peach from the same height. How long does it take

the peach to reach the ground?

6. An arrow fired horizontally at 41 m/s travels 23 m horizontally before it hits

the ground. From what height was it fired?

7. A ball is thrown horizontally from the roof of a building 50. m tall and lands

45 m from the base. What was the ball’s initial speed?

4

(Ans. 7.2 m)

(Ans. 44.1 m and 4.8 m)

(Ans. .37 sec)

(Ans. 1.5 m)

(Ans. 14 m/s)

HorizontallyLaunchedProjectilesActivity

StudentsinGroup:__________________________________________________Pd.#______

ThepurposeofthisactivityistousetheKinematicsEquationswehavelearnedandHorizontal/Verticalanalysisinordertodeterminethelaunchvelocityofahorizontallylaunchedprojectile.PART1-DATACOLLECTIONSetupthewoodenramponyourgroup'slabtable.Youwillberollingaballdowntherampandmeasuringhowfaritlandsfromthebaseofthelabtable(thisiscalledtheRange).Youwillsettherampateachofthefourindicatedheightsinthetablebelow.Foreachheightyousettheramp,youwillrolltheballthreetimes,findtheaveragerangeofyourrolls,andthenusethisdatatocalculatetheinitialhorizontallaunchvelocityfortheball.AllrangemeasurementsaretobeinMETERS!

ProjectileRangeData

LaunchHeight Range1 Range2 Range3 Avg.Range LaunchVelocity

20cm _______m _______m _______m

25cm _______m _______m _______m

30cm _______m _______m _______m

35cm _______m _______m _______m

Below,drawapictureoftheactivityset-up.Showthetrajectoryoftheballasitrollsoffthetableandlandsonthegroundusingadashedline.Showtheballatseverallocationsalongitstrajectoryanddrawthehorizontalandverticalcomponentsofitsvelocity.(Justestimatethelengthofthevectors.)

5

PART2-CALCULATIONSUsethedatayoucollectedtofindtheinitialhorizontalvelocitiesforeachtrial:Trial1:Launchheight20cm:Trial2:Launchheight25cm:Trial3:Launchheight30cm:Trial4:Launchheight35cm:

Besuretogobacktopage1andrecordyouranswersforlaunchvelocityinthetable.

P:

V:

A:

T:

V H

x =

vi = t =

P:

V:

A:

T:

V H

x =

vi = t =

P:

V:

A:

T:

V H

x =

vi = t =

P:

V:

A:

T:

V H

x =

vi = t =

6

ABRHS PHYSICS (CP) NAME: ________________

Introduction to Vectors

side 1

This year in physics, we will study the mathematical relationships between many things. All of these things are either a scalar or a vector. Scalars Quantities that have only a magnitude (tells how much). Examples are distance, speed,

time and mass. Vectors Quantities that have both a magnitude and a direction. Examples are displacement,

velocity, acceleration and force. A good way to think about the difference between these is that a scalar only tells you one piece of information, while a vector gives you two pieces. The scalar speed tells us only how fast something is going, but the vector velocity tells us how fast and in what direction something is going. Scalars are easy - you just give the number and you know everything about it. If the world was one dimensional, vectors would also be easy because you can give directions by using positive and negative numbers (like we have done so far.) To deal with vectors in two or three dimensions, however, you will have to learn a few new tools, because we need to figure out how to deal with two pieces of information for one object. Vector Representation Vectors are a geometrical object - so it is very easy to just think of a vector as an arrow, pointing in a certain direction and the length tells you the magnitude. Two vectors are equal only if they have the same magnitude and the same direction. For example, look at the seven vectors shown below and try and answer the questions that follow:

A B C D E F G 1. Which two vectors have the same magnitude and same direction? 2. What combinations of vectors have the same magnitude, but different directions? 3. What combinations of vectors have the same direction, but different magnitudes? 4. Which vector has the smallest magnitude? Giving Directions One of the main ways of giving directions is to use compass directions - north, east, south and west. To give a direction, you first need to pick a reference (N, E, S, or W). Then figure out how many degrees away from that reference direction the vector is. Finally, figure out which side of the reference direction the vector is pointed. For example, the vector shown in the diagram is going mostly east, so let's call East the reference direction. Notice how the vector is actually pointed 30º away from East. Finally notice that the vector is pointed a little bit North of East. So we the direction is 30º North of East. We could also have said that the vector was going sort of North, and so used that as the reference. Then we would have measured the vector to be 60º away from North, and finally we would have said that it was going to the East side of North. That means we could also have said the direction is 60º East of North. Notice that the angles are complements of each other and that the compass directions are flipped. Either one is fine.

Direction = # degrees which side of reference direction

N

EW

S

30º60º

7

ABRHS PHYSICS (CP) NAME: ________________

Introduction to Vectors

side 2

You will need a ruler and protractor to do these!

5. Determine the magnitude and direction of each of the vectors below: A = B = C = D = E = F = G =

6. Draw each of the given vectors in the space below. A = 5 cm @ 30º N of E B = 10 cm @ 60º N of E C = 8 cm @ 20º N of W D = 7 cm @ 35º W of S E = 5 cm E F = 5 cm @ 15º S of E G = 3 cm @ 40º E of S

N

S

EW

N

S

EW

D

E

F

C

A

B

G

8

6 cm

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PMath 10 - Mr. Duncan

ID: 1

Name___________________________________

Sine, Cosine, and Tangent PracticeFind the value of each trigonometric ratio. Express your answer as a fraction in lowest terms.

1) sin

C

20

2129

C B

A

2) sin

C

40

3050

C B

A

3) cos

C

36

1539

C B

A

4) cos

C

8

1517

C B

A

5) tan

A

35

1237

A B

C

6) tan

X

27

3645

X Y

Z

-1-

9

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Find the value of each trigonometric ratio to the nearest ten-thousandth.

7) sin 62° 8) sin 14°

9) cos 60° 10) cos 31°

11) tan 79° 12) tan 25°

Find the missing side. Round to the nearest tenth.

13) x

1759°

14) x

17 60°

15)

x

20

27°

16)

10

x

51°

17)

20

x

40°

18) x 12

53°

-2-

10

(Ans. 14.6) (Ans. 14.7)

(Ans. 17.8) (Ans. 15.9)

(Ans. 23.8) (Ans. 15.9)

©G SKMuGtdaH wSho6f1tawQaWrUeE WLyLoCb.z 2 XAMl6lh jrfikgPhKtrst WrGetsRePrVv0erdn.D 1 5MAaDdpeg KwbiLtyhV TIunwfYi1nOistdev SAYlNggejbcrjaY Z16.C Worksheet by Kuta Software LLC

Find the measure of the indicated angle to the nearest degree.

19)

39

44?

20) 26

33?

21) 24

36

?

22) 20

23?

23) 3310?

24)

1613

?

Find each angle measure to the nearest degree.

25) sin X = 0.7547 26) sin A = 0.4540

27) cos Y = 0.5736 28) cos B = 0.5000

29) tan B = 0.6249 30) tan C = 0.1405

-3-

11

(Ans. 62.4∘) (Ans. 52∘)

(Ans. 48.2∘) (Ans. 29.6∘)

(Ans. 16.9∘) (Ans. 39.1∘)

(Ans. 49∘) (Ans. 27∘)

(Ans. 55∘) (Ans. 60∘)

(Ans. 32∘) (Ans. 8∘)

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Solve the following word problems. For each question, draw a diagram to help you.

31) An airplane is flying at an altitude of 6000 m over the ocean directly toward a coastline. At a certaintime, the angle of depression to the coastline from the airplane is 14°. How much farther (to thenearest kilometer) does the airplane have to fly before it is directly above the coastline?

32) From a horizontal distance of 80.0 m, the angle of elevation to the top of a flagpole is 18°. Calculatethe height of the flagpole to the nearest tenth of a metre.

33) A 9.0 m ladder rests against the side of a wall. The bottom of the ladder is 1.5 m from the base of thewall. Determine the measure of the angle between the ladder and the ground, to the nearest degree.

34) The angle of elevation of the sun is 68° when a tree casts a shadow 14.3 m long. How tall is the tree,to the nearest tenth of a metre?

35) A wheelchair ramp is 4.2 m long. It rises 0.7 m. What is its angle of inclination to the nearestdegree?

36) A person flying a kite has released 176 m of string. The string makes an angle of 27° with theground. How high is the kite? How far away is the kite horizontally? Answer to the nearest metre.

-4-

12

(Ans. 26 m )

(Ans. 80.4∘)

(Ans. 35.4 m )

(Ans. 9.6∘)

(Ans. 80m ; 157m )

ABRHS PHYSICS (CP) NAME: ________________

Vector Components

side 1

Thinking about vectors as a magnitude and a direction is the most natural and obvious way, but it turns out that it is not always the easiest way. When we are dealing with vectors in this class, we will usually deal with the components of the vector. Each vector has two components. We could call them the East and North components, or the horizontal and vertical components, or even the x and y components. Components The parts of a vector that are going East/West and North/South. Or we could say the

part of a vector that is going vertical and the part of a vector that is horizontal. Remember that we have to give two pieces of information to describe a vector. Instead of thinking of a vector as a magnitude and a direction, we can think of how much of the vector going left or right and how much of the vector is going up or down. Put another way, the components of a vector are the two special perpendicular vectors that add up to the vector we want. Look at the picture below:

A

BC

Notice how C is the resultant of A + B. Also notice how A and B are perpendicular to each other and that A is going to the right and B is going up. We could describe A as being due East or horizontal or perhaps just say in the "x"-direction. Likewise, We could describe B as being due North or vertical or perhaps just say in the "y"-direction. A and B are the components of C. The magnitude of the vector is just the length of vector C. When we use vectors, we decide whether to use East/North or horizontal/vertical or x/y based on the wording of a problem. 1. Some vectors are shown in the grid below. Give the x and y components of each vector.

A BC D

E

FG

H

I

Ax = _____ & Ay = _____ Bx = _____ & By = _____ Cx = _____ & Cy = _____ Dx = _____ & Dy = _____ Ex = _____ & Ey = _____ Fx = _____ & Fy = _____ Gx = _____ & Gy = _____ Hx = _____ & Hy = _____ Ix = _____ & Iy = _____

13

Name __________________________________________ Period ____ Date _____  Component & Protractor Practice 

Draw in the x & y components of the following resultant vectors.   

    

14

Name _________________________ Date ______________

Vector Components Worksheet

(HS5.1.1.4) 1. Using dotted lines, draw the horizontal and vertical components for each vector shown below. Show only one pair of the components.

2. Using the angles given on the diagrams in problem #1 above, calculate the values of the horizontal ( x ) and vertical ( y ) components for each diagram you did above, showing your work in the box for each below. Note: Be sure your calculator is in “DEGREE” mode before doing your calculations. X = Y =

X = Y = X = Y =

X = Y =

X = Y = X = Y =

X = Y =

X = Y = X = Y =

40 m, 40o from horizontal 9 lb, 20o from hroizontal 20 km 15o from vertical

15 m/s, 50o from vertical 45N, 70o from vertical 15 ft, 80o from horizontal

6 mi, 0o from vertical 50 m/s2, 0o from horizontal 100 m/s, 30o from horizontal

15

FindingResultantVectorsFromComponentsForeachsetofcomponentsgivenbelow,drawtheresultantvector,thenfinditsmagnitudeanditsdirection.Note:Allcomponentshavemagnitudesthatareeitherwholenumbervaluesor

halfnumbervalues.Ex.3,2.5,7,8.5,etc.

16

1

Projectiles Launched at an Angle – Note Sheet Physics Types of Projectiles Launched at an Angle Now we will analyze the motion of a projectile that is launched at an angle. The projectile could be launched off a cliff at an angle and then fall to some point below the cliff OR be launched from ground level and return to ground level Consider a cannonball shot at an upward angle. If there were no gravity, the ball (would/would not) fall toward earth, but would rather follow the path indicated by the _____________ line. However, there is gravity on earth, so what really happens is the ball continually falls beneath the imaginary dashed line until it strikes the ground. It should not be surprising that the vertical distance is falls is (the same/not the same) as the distance it would fall if it were dropped from rest at that position. This distance would be found using the equation ___________________. Likewise, the time it would be falling through the air (would be/would not be) the same as if it were dropped from rest.

The main difference between projectiles launched horizontally off a cliff and those launched at an angle is that the initial vertical velocity of the object IS NO LONGER ________________. Notice the sketch of the girl throwing the stone at an upward angle. In a problem, you would be given only the resultant velocity of the projectile and the angle at which it was launched. Before beginning the problem you will have to ______________________ the resultant velocity into its ____________________ and ___________________________ components. This is done using the sine and cosine functions. The horizontal component is found using _______________________, while vertical components is found using _______________.

Look at the diagram of this projectile launched at an angle. Notice: 1. The _______________ component (vx) of the velocity is the same everywhere! 2. The vertical component (vy) of the velocity is the same as if it had been thrown upwards with vo = _________! As it rises, its velocity ________________ with time as it goes _________________ gravity. When it reaches its highest point, its vy = _______. As it falls from its highest point vy (increases/decreases) as it travels with gravity. Its vertical velocity can be determined just like an object that is _________________.

17

ProjectilesLaunchedfromaHeight

1.Acatjumpsoffatablewhichis1.5mhigh.Iftheinitialvelocityofthecatis10m/s,atan

angleof37ºabovethehorizontal,howfarfromthebottomofthetabledoesthecatland?

2.Asnowballisthrownoutasecondstorywindow(7mhigh)withaspeedof32m/s.Itis

thrownatanangleof57°abovethehorizontal.

a.Whatistheball'sinitialhorizontalvelocity?

b.Whatistheball'sinitialverticalvelocity?

c.Howlongistheballintheair?

d.Howfarawayfromthebuildingdidtheballland?

3.Whilesittinginatree,Tarzantriedtogetatrapper'sattentionbythrowingabananawitha

velocityof20m/sata30degreeanglebeneaththehorizontal.HowhighwasTarzanifthe

bananatook2secondstohittheground?(Notice:Initialverticalvelocitywillbenegative.)

4.Arockisthrownoffatallbuildingat45m/satanangleof30°belowthehorizontal.(Notice:

Initialverticalvelocitywillbenegative.)

a.Howlongistherockinair?

b.Howfarfromthebuildingdidtherockland?

5.Arockisthrownoffatallbuildingat45m/satanangleof60.0°abovethehorizontal.

a.Howhighdidtherocktravel?

b.Howlongistherockinair?

c.Howfarfromthebuildingdidtherockland?

18

**Use a height of 50m for the building in problems 4 and 5**

Projectile Motion Worksheet - Ground Level Launch

1) A baseball player leads off the game and hits a long home run. The ball leaves the bat at an angle of 30.0o from the horizontal with a velocity of 40.0 m/s. How far will it travel in the air? [141 m]

2) A golfer is teeing off on a 170.0 m long par 3 hole. The ball leaves with a velocity of 40.0 m/s at 50.0o to the horizontal. Assuming that she hits the ball on a direct path to the hole, how far from the hole will the ball land (no bounces or rolls)? [9.38 m]

3) A punter in a football game kicks a ball from the goal line at 60.0o from the horizontal at 25.0 m/s.

a) What is the hang time of the punt? [4.41 s] b) How far down field does the ball land? [55.2 m]

4) A cannon fires a cannonball a 500.0 m range when set at a 45.0o angle. At what velocity does the cannonball leave the cannon? [70.0 m/s at 45.0o]

19

ProjectilesLaunchedatanAngleWorksheet

1.Asoccerballiskickedoffthetopofabuilding90mtallatanangleof67otothehorizontal.Ifitsinitialvelocityif4.5m/s,howfarwillitlandfromthebaseofthebuilding?2.Asquirrelleapsfromthebranchofatreeatanangleof25otothehorizontal.Ifitsinitialvelocitywas3m/sanditlandsontheground20mfromthebaseofthetree,howtallisthetree?3.Tarzandivesoffa50mcliffintothewaterbelow.Heleavesthecliffatanangleof37otothehorizontalandlandsinthewater36mfromthebaseofthecliff.Whatwashisinitialvelocity?4.Afootballiskickedupwardfromthegroundatanangleof30owithavelocityof4.7m/s.Whatmaximumheightwillitreachandhowlongwillittaketohittheground?5.A ball is shot out of a slingshot with a velocity of 10.0 m/s at an angle of 40o above the horizontal. How far away does it land?

20

(Ans. 8.3 m)

(Ans. 259 m)

(Ans. .28 m ; .48 sec )

(Ans. 10 m)

ProjectilesReviewWorksheet

1.A lemming running 2.3 m/s dives out horizontally from the edge of a vertical cliff and reaches the water below 4.2 s later. How high was the cliff? (Ans. 86.4 m) 2.A stone is thrown from ground level with a velocity of 8 m/s at an angle of 20o above the horizontal. How far away does it land? (Ans. 4.1 m) 3.Supermanjumpsoffabuildingandlandsinthestreetbelow.Ifheleavesthebuildingatanangleof52otothehorizontalandlands73mfromthebaseofthebuilding3secondslater,whatwashisinitialvelocity?(Ans.39.5m/s)4.Asoccerballiskickedupwardfromthegroundatanangleof28owithavelocityof6m/s.Whatmaximumheightwillitreach?(Ans..4m)5Amanleapsfromthebranchofatreeatanangleof38otothehorizontal.Ifhisinitialvelocityis2.8m/sandhelandsontheground13mfromthebaseofthetree,howtallisthetree?(Ans.161m)6. A jaguar leaps horizontally from a 5.9 m high rock with a speed of 3.5 m/s . How far from the base of the rock will he land? (Ans. 3.9 m) 7.A watermelon is thrown horizontally from the roof of a building 87 m tall and lands 15 m from the base. What was its initial speed? (Ans. 3.6 m/s) 8.Ateakettleiskickedoffthetopofabuilding105mtallatanangleof46otothehorizontal.Ifitsinitialvelocityis1.3m/s,howfarwillitlandfromthebaseofthebuilding?(Andwillwestillbeabletomaketea?)(Ans.4.2m)

21

GeneralandHonorsPhysics:Unit2TestReviewSheet

1.Findthetrigonometricfunctionforthegivenangleindicated:

Ans.[.6] Ans.[.3429] Ans.[.4706]

2.Findx:

Ans.[17.8] Ans.[14.7] Ans.[15.9]

3.Findthemissingangle:

Ans.[48.2o] Ans.[39.1

o] Ans.[52.0

o]

4.FIndtheXandYcomponentsofthevectordescribed:

a)47m/sat34oabovethehorizontal b)135mat67

oNofE c)23m/s

2at280

ofromthexaxis

[X:39.0m/sY:26.3m/s] [X:52.7m,Y:124.3m][X:4m/s2,Y:-22.7m/s

2]

5.Edwinakicksarockhorizontallyoffofa30mhighcliff.Howfastdidshekicktherockifithitstheground

37mfromthebaseofthecliff?Ans.[15m/s]

6.Nicolethrowsaballfromgroundlevelat20m/satanangleof65°abovethehorizontal.Whatistherange

oftheball?Ans.[31m]

7.Acannonfiresaprojectilefromgroundlevelat75m/satanangleof56°abovethehorizontal.What

maximumheightdoestheprojectilereach?Ans.[197.4m]

8.Aballisshotoffacliffwithavelocityof10.0m/satanangleof40oabovethehorizontal.Itlandsadistance

of50mfromthebaseofthecliff.Howlongwasitintheair?Howtallisthecliff?Ans.[6.5s,167m]

22

9.Agolfballislaunchedfromgroundlevelwithaninitialvelocityof25m/sandlandsontheground4secondslater.Fromwhatanglewasitoriginallylaunched?Ans.[51.6o]10.Findtheresultantvelocitiesforeachsetofcomponentsbelow:[9.4m/sat32oNofE][20.6m/sat76oNofE][9.8m/sat24oSofE][31.6m/sat18.4oNofE]HONORSONLY:11.Aballisthrownfromgroundlevelatanangleof35oandaninitialvelocityof12m/s.Whatisitsvelocityafter.38seconds?Whatisitsvelocityatmaximumheight?Withwhatvelocitywillithittheground?(AllVelocitiesMagnitudesOnly)Ans.[10.3m/s,9.8m/s,12m/s]12.Aplanehasavelocitywithcomponents175m/sSouthand235m/sWest.a)Whatistheplane'sresultantvelocity?(MagnitudeandDirection.)Ans.[293m/sat36.7oSofW]b)WhatdistanceSouthhastheplanetraveledafter10minutes?Ans.[105,000m]c)Howfarawayfromitsstartingpointistheplaneafterahalfhour?Ans.[527,400m]13.Aballrollsoffatablehorizontallywithavelocityof5m/sandlandsonthefloor6.2mfromthebaseofthetable.Whatistheball'svelocity(magnitudeonly)whenithitstheground?Ans.[13.2m/s]14.Aballiskickedfromgroundlevelintotheairatanangleof63o.Itlands32maway.Whatwasitsinitialvelocity?Ans.[19.8m/s]15.Withwhatinitialhorizontalvelocitymustthisrunnerleavethecliffinordertoexactlylandattheedgeoftheledgebelow?Ans.[2.18m/s]

3.412

23

SUPPLEMENTAL MATERIALS

(ADDITIONAL PRACTICE)

Vectors and Right Triangle Trigonometry

For Mr. Wayne’s Students (2014 Edition) Another fine worksheet by T. Wayne 20

For each vector drawn below on a coordinate axis, label the shown θ with it proper compass headings, e.g. N of W, S, S of E, etc.

θ

1

θ

2

θ

3

θ

4θ

5

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Practice Naming Vector DirectionsPractice Naming Vector Directions

Vectors and Right Triangle Trigonometry

For Mr. Wayne’s Students (2014 Edition) Another fine worksheet by T. Wayne 21

For each vector drawn below, calculate its magnitude and direction. NOTE: For the vector’s direction, there will be two possible correct answers for each problem. The two answers are complimentary to each other.

1 2 3 4 5 6 7

8 9 10 11 12 13 14

15 16 17 18 19 20 21

22 23 24 24 26 27 28

29 30 31 32 33θ

34 35

36 37 38 39 40 41 42

43 44 45 46 47 48 49

50 51 52 53 54 55 56

Solving Vectors

Find the magnitude and angle of the resultant. 1. 2.

3. Bill drives 14 miles North, then 5 miles East, then 4 miles South. a. What is his total distance traveled? b. What is Bill’s displacement (magnitude and direction).

Find the horizontal and vertical components of each vector. 4. 5. 6. A plane taking off is traveling 225 m/s at an angle of 22 degrees with the ground.

Calculate the horizontal and vertical components of its velocity.

6 mi

9 mi

32 m

25 m

28o

42 mph yv

xv

Horizontal Velocity Vertical Velocity

50o

12 m/s

yv

xv

Horizontal Velocity Vertical Velocity

Find the magnitude and direction of the resultant. Assume the tail of the resultant is at the origin of an X/Y coordinate system. Find the magnitude and direction of the resultant. Assume the tail of the resultant is at the origin of an X/Y coordinate system.

Projectile Motion Worksheet - Horizontal Launch

1) A ball rolls with a speed of 2.0 m/s across a level table that is 1.0 m above the floor. Upon reaching the edge of the table, it follows a parabolic path to the floor. How far along the floor is the landing spot from the table? [0.90 m]

2) A rescue pilot drops a survival kit while her plane is flying at an altitude of

2000.0 m with a forward velocity of 100.0 m/s. If air friction is disregarded, how far in advance of the starving explorer’s drop zone should she release the package? [2020 m]

3) A rifle is fired horizontally and travels 200.0 m [E]. The rifle barrel is 1.90 m from the ground. What speed must the bullet have been travelling at? Ignore friction. [321 m/s]

4) A skier leaves the horizontal end of a ramp with a velocity of 25.0 m/s [E] and lands 70.0 m from the base of the ramp. How high is the end of the ramp from the ground? [38.5 m]

5) An astronaut stands on the edge of a lunar crater and throws a half-eaten Twinkie™ horizontally with a velocity of 5.00 m/s. The floor of the crater is 100.0 m below the astronaut. What horizontal distance will the Twinkie™ travel before hitting the floor of the crater? (The acceleration of gravity on the moon is 1/6th that of the Earth). [55.3 m]

25

Chapter 3 Projectiles Worksheets

1. A bullet shot at 800. m/s horizontally hits a target that is 180. m away. How far does the bullet fall before it hits the target?

[0.250 m]

2. A student throws a ball (horizontally) out of a window that is 8.0 m above the ground. Another student who was 10.0 m

away caught it. What was the initial velocity of the ball?

[7.8 m/s]

3. Maverick and Goose are flying a training mission in their F-14. They are flying at an altitude of 1500. m and are traveling at

688 m/s (mach 2). They release their bomb and head for home.

A. How long will it be before the bomb hits the ground?

B. How far (on the ground) from where they released it will it land?

1500 m

A. [17.5 s]

B. [12040 m]

26

8. A football is kicked on flat ground at a velocity of 15 m/s at an angle of 25q.

A. How long will it be in the air?

B. How far away will it land?

C. How high will it go?

D. What will be its velocity after 0.25 s?

E. What other angle will produce the same range?

A. 1.3 s

B. 18 m

C. 2.1 m

D. 14.1 m/s

E. 65q

9. A soccer ball is kicked at 8.0 m/s. It lands on the ground after being in the air for 0.85 seconds. At what angle was it kicked?

Assume level ground…..

8 m/s

[31.4°]

27

10. A peanut slide off a chute at 12 m/s.

a. Find time in air. [1.1 s]

b. Range (R). [13.3 m]

11. For the kicked ball find:

a. Time in air. [1.02 s]

b. Range. [8.8 m]

c. Maximum height. [1.3 m]

d. Velocity (resultant) after 0.20 seconds. [9.5 m/s]

28

12. Find vA

50°

45 m

[21.2 m/s]

13. A football is kicked as shown.

a. How long will it be in the air? [1.04 s]

b. How high will it go? [1.4 m]

c. What will be its resultant velocity after 0.80 s? [6.7 m/s]

29

14. A tennis serve is hit horizontally with a velocity of vA.

a. Calculate the time the ball takes to get to B? [0.535 s]

b. Calculate vA. [12 m/s]

c. Calculate how far from the net (s) will it land? [1.7 m]

2.3 m

0.9 m

6.5 m

15. A motorcycle leaves the ramp at an angle of 30° as shown. It is in the air for 1.5 seconds.

a. What was its velocity when it left the ramp? [13 m/s]

b. How far away will it land (R)? [17 m]

30

16. Indiana Jones is running from his enemies. How fast (v0) is he running if he lands at the edge of the

ledge as shown:

[1.29 m/s]

17. A ball is thrown at 25 m/s as shown below. The wall is 11 m from the person.

a. How long will it take for the ball to reach the wall? [0.52 s]

b. How high up the wall will it hit? [5.6 m]

32°

11 m

31

18. An airplane is traveling at vA = 67 m/s at an altitude of 500 m. It drops a box of supplies when it is

directly over a polar bear.

A. How long will the box be in the air? [10.1 s]

B. How far from the polar bear will it land? [677 m]

C. What will be the velocity of the box when it strikes the ground? [120 m/s]

500 m

19. Determine the velocity of the dirt bike as it left the ground.

6.0 m

[8.2 m/s]

32