a 2 + b 2 = c 2 tan θ = opp/adj (typically used to find the angle) cos θ = adj/hyp (typically used...

a2 + b2 = c2

Tan θ = opp/adj (typically used to find the angle)Cos θ = adj/hyp (typically used to find the x component)Sin θ = opp/hyp (typically used to find the y component)

10/9Test Grades will be posted by the end of 8th period.You may come in today after school to see test &/or start

test corrections. I will also be available Fri am, Tue,Wed, Thu am & pm.

NOW: Pick up graph paper and protractor. Have Notes out.Test make ups were yesterday and today after school Yesterday we took notes on vector diagrams and completed

the Vector diagram WS. If you were absent, complete this and turn into me. Make sure to follow tip to tail rule.

10/10Test Grades were posted Thursday.You may come in today for test corrections Friday until

12:45, Tue,Wed, & Thu am & pm. Final Test retake Thur pm.

Test make ups will be available today after school until 12:45 and Tuesday after school. NO test make ups after Tuesday

Yesterday we completed graphing examples 1 & 2 in your notes. Ex 3 & 4 were to be completed in class & home.

NOW: Pick up graph paper,protractor and calculator. Have completed ex 3 & 4 out to be checked.

10/14I am available for test corrections Tue,Wed, & Thu am &

pm. Final Test retake Thur pm.Test make ups will be available today after school. NO

test make ups after Tuesday (2:50-4)Friday I checked graphing examples 3 & 4 in your notes.

These were assigned Thursday 10/9. We then looked at graphing multiple vectors.

NOW: Julie slams on the brakes of her car moving at 24 m/s and skids to a stop in 8 s.

What is the deceleration rate of the car? (5pts) How far does it skid? (5pts)

10/14 NOW: Julie slams on the brakes of her car moving at

24 m/s and skids to a stop in 8 s. What is the deceleration rate of the car? (5pts) How far does it skid? (5pts)

d = ? A) a = vf – vi = 0 m/s - 24 m/s = -3 m/s 2

vi = 24 m/s t 8 s

vf = 0 m/s

a = ? B) d = vi t + .5at2

t = 8 sec d = (24 m/s)(8s) + [(.5)(-3m.s2)(8s)2

d = 96 m

10/16I am available for test corrections Thu, Fri and Mon am & pm.

Final Test retake Mon pm. (I extended time)If you chose not to work on test corrections in class yesterday

you have lost the opportunity to do test corrections for the trig test. (Trig Review Website, Youtube mrsseeb239)

Next Tue is the Vector Test. Don’t forget BOPS if interested.Today we will look at components and riverboats. Pick up Vector

WS II. Have your notes and calculator out. NOW: Josh drops an apple from a rocket on the

moon. The ag on the moon is 1.6m/s2. How fast will it be falling after 8 seconds? What distance will it have fallen in 8 seconds?

10/16 NOW: Josh drops an apple from a plane.

How fast will it be falling after 8 seconds? What distance will it have fallen in 8 seconds?

d = ? A) vf = vi + at 0m/s + (1.6 m/s2 )(8s)

vi = 0 m/s = 12.8 m/s

vf = ?

a = 1.6 m/s2 B) d = vi t + .5at2

t = 8 sec d = (0 m/s)(8s) + [(.5)(1.6m.s2)(8s)2

d = 51.2 m

10/16 NOW: Josh drops an apple from a rocket.

d = ? A) vf = vi + at 0m/s + (1.6 m/s2 )(8s)

vi = 0 m/s = 12.8 m/s

vf = ?

a = 1.6 m/s2 B) d = vi t + .5at2

t = 8 sec d = (0 m/s)(8s) + [(.5)(1.6m.s2)(8s)2

d = 51.2 m

10/17 Vector Test on Tuesday 10/21 Pick up Review Sheet and calculator

Yesterday we covered ex 5-7 in the vector notes. Remember the Power point and BOPS are posted under the vector tab. You then were given some time to work on Vector WS II.

Next Thursday in class the Physics department is offering a retest on the Trigonometry test for all students to improve their grade. You do not have to have completed test corrections to take this retest. If you are satisfied with your previous test grade, you can opt out of taking the test. If you take the retest on Thursday, the better score of the two tests will be recorded in gradebook. BOPS do not apply to the retest.

Solve Now: What is the sin of 30º? What does this mean? If the hypotenuse for this ∆ was 10cm, what is the opposite side?

10/17Vector Test on Tuesday 10/21Yesterday we covered ex 5-7 in the vector notes. Remember the Power point and BOPS

are posted under the vector tab.You will be able to have access to your notes. You will place notes only (not your

review,worksheets or labs) at the back of the room. They must have your name on them in ink. IF you choose you may print out a copy of my notes. They must have your name on them in ink & I must see these and initial them. It may be a good idea to show them to me on Monday so as not to interfere with your testing time. You may look at them up to 3 times. You may not bring any paper or writing instruments when you look at them. I will return them to you the following day. This is not a substitution for studying and you only have the class period to complete the test.

Next Tue is the Vector Test. Don’t forget BOPS if interested.Today we will look at components and riverboats. Pick up Vector WS II. Have your notes

and calculator out.

NOW: Josh drops an apple from a rocket on the moon. The ag on the moon is 1.6m/s2.

If you chose not to work on test corrections in class yesterday you have lost the opportunity to do test corrections for the trig test. (Trig Review Website, Youtube mrsseeb239)

Today you will complete the pirate vector labToday you will complete the pirate vector lab

You will work in pairs. Supplies: Large piece of paper Metric ruler Protractor Colored Pencils or markers Lab directions There are 12 clues

Pirate Vector lab Scoring (20 pts):Pirate Vector lab Scoring (20 pts):

Compass Rose (1 pt)Scale (1 pt)All vectors labeled, with arrows (2 pts)

Drawings x 3 (6 pts) DR labeled (with arrow) (3 pts)

Correct DR (+/- 0.5cm) (3 pts) Indicate DR = in blank area. Include units (paces)

Secret Rule (2 pts) Indicate blank area Neatness (2 pts) Bonus: Determine angle and direction: Show work (2 pts)

10/1010/10You walk 5m E10m S3m W4m S7m w2m NWhat is your distance?

What is your displacement?

Scale: 1cm = 1 m

NW E S

Scale: 1cm = 1 m

NW E S

Scale: 1cm = 1 m

NW E S

10/1010/10You walk 5m E10m S3m W4m S7m w2m NWhat is your distance? 31m

13m at 22.62º WofS

Scale: 1cm = 1 m

NW E S

Motion VectorsMotion Vectors

10/8 Tests will be graded by Friday at the latest

Pick up both sheets at front

Test Make Ups today and Thursday after school!Corrections/retakes next Tue-ThuCorrections am & pmRetakes pm only

NOTICEFor the remainder of the year, to be eligible for test corrections, you must show me a copy of your class notes. They must have your name and period on them and I must initial them.

What is the difference between a vector and a scalar quantity?

VectorsVectors

Quantities with magnitude, unit, and direction What are some examples: Displacement Velocity Acceleration Force

Scalar Quantity- has only a magnitude and a unit.

Example- 10 km/hr N is vector while 10km/hr is a scalar

A picture is worth a 1000 words..Motion diagrams

Arrows represent vectors Connect the tail of one vector to the arrow tip of

the other

Applies to all motion vectors

Motion DiagramsMotion Diagrams

A person walks east on a moving sidewalk going east

A person walks east on a moving sidewalk going west

A bug crawls north then eastA bug crawls north then east

A car accelerates to the south then accelerates going to the west

Practice drawing motion diagramsPractice drawing motion diagrams

Motion Vector Diagram WS

Do they only indicate direction? No They can indicate magnitude They can be used to determine the overall

displacement, velocity, etc. Vectors are being “added” This is called the Resultant

Motion Diagrams can indicate more!Motion Diagrams can indicate more!

Arrows represent vectors Length of arrow corresponds to magnitude of vector Connect the tail of one vector to the arrow tip of the other No matter what route you take from point A to point B

your final displacement vector will be the same The final displacement vector is called the resultant

vector Draw in the resultant vector from the tail of the first

vector to the arrow head of the second

Applies to all motion vectors

Remember: Motion DiagramsRemember: Motion Diagrams

Practice adding vectors Ex 1Practice adding vectors Ex 1 Draw the following to scale:

Indicate scale and compass rose.Make sure you draw tail to tip for the two vectors.Indicate the resultant with a dotted line. The tip of the resultant meets the tip of the second vector.You walk 5 m to the north and then 8 m eastDetermine your resultant displacement graphically.What did you get? I got 9.7m.

Ex 1Ex 18 m

Ex 1Ex 1Determine your resultant displacement graphically.What did you get? I got 9.7m.

Ex 1Ex 1

“θ” or Theta, is any unknown angle but in this case it is the angle between the two vectors

Use a protractor to determine the angle “θ” of your resultant.Place the protractor along the axis of the initial vector. Take the reading in reference to the resultant.Refer to diagram on next slide

Ex 1Ex 1

What value did you get with your protractor?I got 59°This would be described as 59° east of north since the resultant is east of the north axis.

WHICH ANGLE?WHICH ANGLE? Describe angle in reference to vertical vector

compared to horizontal vector: N of E

Describe angle in reference to horizontal vector compared to vertical vector: E of N

How are these 2 angles related?

Ex 1Ex 1 Solving resultant mathmatically: How?

Determine your resultant displacement using the Pythagorean formula.Did you get 9.43 m?

Ex 1Ex 1

θAdj5m

Opp 8m

Ex 1Ex 1Solve angle mathematically: How?Use SOH CAH TOALabel the sides in reference to θ.I would suggest using tan in case you measured the hypotenuse incorrectly. Using Tan-1:Θ Tan-1 (8m/5m) = You should get 57.99° The direction is still East of NorthThis is in the same range as what we got with the protractor.

Practice adding vectors Ex 2Practice adding vectors Ex 2 Draw the following to scale:

A car travels 4 m/s west then 7 m/s southDetermine your resultant velocity graphically.What did you get?I got 8.2 m/sDetermine your resultant displacement using the Pythagorean formula.Did you get 8.06 m/s?

Ex 2Ex 2 4 m/s

Ex 2Ex 2

Use a protractor to determine the angle “θ” of your resultant.Place the protractor along the axis of the initial vector. Take the reading in reference to the resultant.Refer to diagram on next slide

Ex 2Ex 2 Adj 4 m/s

Opp7 m/s

Ex 2Ex 2

What value did you get with your protractor?I got 60° This would be described as 60° south of west since the resultant is south of the west axis.How could you do this mathematically?Use tanLabel the sides in reference to θ.

Ex 2Ex 2Using Tan-1:Θ Tan-1 (7m/s /4m/s) = You should get 60.26° The direction is still South of WestThis is in the same range as what we got with the protractor.

Practice adding vectors Ex 3-4Practice adding vectors Ex 3-4

Perform the following examples: Ex 3 You walk 8 meters south, then 3 meters east. Ex 4. You run at 8 m/s to the east, then 2 m/s to the

south. Ex 3 Displacement = 8.54 m at 20.56º E of S Ex 4 Displacement = 8.24 m at 14.04º S of E

What are Components?What are Components? The sides that make the resultant

vector …the legs

Ex 5 ComponentsEx 5 Components You are given a

resultant vector of 8 m/s at 30° N of E We are going to work

backwards! Draw in the y

component Draw in the x

component How would you

determine these?

Ex 5 ComponentsEx 5 Components y: opp = (sinθ)(hyp)

opp = sin(30°)(8 m/s) y = 4 m/s

x: adj = (cosθ)(hyp) adj = (cos30°)(8m/s) x = 6.9 m/s

These are pretty close to our graphical values.

Ex 6: You are given a resultant vector of 6.0 m/s at 10° N of WWhat is the northern component?What is the western component?Draw the diagram. Solve mathematically

Northern: O= SH O = sin(10º)(6.0 m/s) = 1.04 m/s

North Western: A = CH A = cos(10º)(6.0 m/s) = 5.91 m/s West

Special SituationsSpecial Situations NW, SW, NE, SE all indicate angles of? 45° Due North or due South indicates what

angle? 90° Due East or due West indicates what

angle? 0°

Sketch the followingSketch the following

3.5 m/s due South 8 m/s due East 6 m/s at 10° North of East

Why do Components?Why do Components?

Ex. 7 Lets say you are on a

hike and walk 3.5 m due south. You then turn and travel 8m due east. After resting you conitinue on for 6 m due north. What is your total distance? What is your resultant displacement in respect to the earth?

Ex. 7 Lets say you are on a

hike and walk 3.5 m due south. You then turn and travel 8m due east. After resting you conitinue on for 6 m due north. What is your total distance? What is your resultant displacement in respect to the earth?

Ex. 7What is your totaldistance? That is easy-just add up all the distances: 3.5 + 8m + 6m =

Ex. 7What is your resultantdisplacement inrespect to the earth?

Displacement is the shortest distance between start and finish:

Why do Components?Why do Components? Where is your start

and finish? How would you determine displacement?

Do you see thetriangle?Can you determine the sides?How would you calculate the Displacement? What about direction?

Make theTriangle.Determine the

horizontal and vertical components.

Determine resultant Displacement? What about direction?

Quick CheckQuick CheckHow do you determine total distances?Add the components, do not consider direction (signs)Do not include the resultantWhen should I include angles and direction on problems?Anytime that you are working with a vector. Remember vectors have magnitude and directionWhen do you use the sin, cos, & tan keysWhen you have the angle and are looking for the ratio or a sideWhen do you use the sin-1, cos-1, or tan-1 keys?When you have two sides and are looking for the angle

Quick CheckQuick CheckHow do you determine the resultant of two vectors at a right angle?Pythagoreans TheoremHow do you determine the components of a resultant when given the magnitude and angle/direction of that resultant?Use cos(Θ)(H) for the adjacent side. Typically the X or horizontal axisUse sin(Θ)(H) for the opposite side. Typically the Y or vertical axis

ConceptConceptYou are floating in a river. If you do not paddle, what

determines how far downstream you go in 60 seconds?What if you were paddling straight across the river, how

would this change?

Example 8Example 8 A girl scout elects to swim across the river. The river is

37.5 meters wide. A current flows downstream at a rate of 0.66 m/s. If she initially swims towards the boy scout camp (directly cross the river) at a rate of 1.73 m/s, how long will it take her to reach the far shore?

Remember what the question asks. How long does it take her to swim across? To solve for time, what do we need to know? Use velocity and displacement but only in reference to

crossing the river.

] 37.5m

1.73 m/s

vgs = dr/tt = dr/vgs t = 37.5m÷1.73m/s t = 21.7 s

] 37.5m

1.73 m/s

Where exactly does the girl scout end up on the far shore?

What do we need to know?To determine displacement we need velocity

and time but only in reference to downstream.

] 37.5m

1.73 m/s

Example 8

To find where she ends up, what is the downstream velocity? 0.66m/s What is the time? 21.7 sec Time is the same for both cross stream and downstream. 14.3 m downstream

0.66m/s

When working with multiple vectors remember they are independent of one another although they have a net effect.

In the case of the girl scout, her overall (think resultant) velocity and direction changed.

Do you know how to solve for the apparent resultant velocity and direction?

Resultant velocity? Make sure you only use velocity vectors!

c2 = 1.732 + 0.662

c = 1.85 m/s Which angle for direction? θ Tan-1 = (0.66m/s / 1.73m/s) θ = 20.88° vr = 1.85 m/s at 20.88° downstream in respect to

motion

0.66m/s

1.73 m/s c

Resultant velocity? Make sure you only use velocity vectors!

c2 = 1.732 + 0.662

c = 1.85 m/s Which angle for direction? θ Tan-1 = (1.73m/s / 0.66m/s) θ = 69.1° vr = 1.85 m/s at 69.1° downstream in respect to shore

0.66m/s

1.73 m/s c

Resources

Extend (Choose the activity most appropriate for your class)

Lab: Vector Webquest http://www.west.asu.edu/achristie/548/02WQ/ronni/VectorWebQuest.htm

Treasure map Lab

http://www.richtherrn.org/physics/vectorlab.htm

The Paper River Lab

Refer to Glencoe Physics page 69

What are the values for X & Y in each quadrant ?What are the values for X & Y in each quadrant ?

X is +

Y is +

X is -

Y is -

X is +

Y is -

X is -

Y is +

Ex 5 ComponentsEx 5 Components Determine the

magnitude of x and y graphically.

y = 4 m/s north x = 7 m/s east 30°

Ex 5ComponentsEx 5Components Can you determine

the magnitude of x and y using math?

Visualize a triangles. Name the sides in reference to the 30°angle and use Sine and Cosine to solve for the sides.

ComponentsComponents Try these on your

own: 3.5 m/s due South 8 m/s due East 6 m/s at 10° North

of East

Given a resultant vector of 22 m/s NE; what are the component vectors?

View the components as representing X & Y values on a graph

22 m/s

Use trig functions to determine values for X & Y. NE = 45 degrees

How would you solve for X? Use cosine How would you solve for Y? Use sine

22 m/s

Example problemExample problem

You walk 7 mile south and then 3 miles west. What is the resultant displacement and how did

you determine it? (7mi)2 + (3mi)2 = r2 where r = the resultant r = 7.62 mi 3mi ÷ 7mi = tanθ θ = 23° W of S

Example problemExample problem A boat can travel 4m/s in still water. It is heading

east at this velocity It is in a river flowing south at 5.5 m/s What is the total (resultant) velocity and direction

of the boat and how did you determine it? vt = boat’s velocity + river’s velocity where vt =

total velocity How do you add this? (4m/s)2 + (5.5m/s)2 = vt

2 where r = the resultant vt = 6.8m/s What about direction? 5.5m/s ÷ 4.0m/s = tanθ θ = 54° South of East

Example problemExample problem An airplane is headed directly east at 340 miles

per hour when the wind is from the south at 45 miles per hour.

What is the total (resultant) velocity in respect to the ground and direction of the plane. How did you determine it?

vt = plane’s velocity + wind’s velocity How do you add this? (340mi/hr)2 + (45mi/hr)2 = vt

2 vt = 343mi/hr What about direction? 45mi/hr ÷ 340mi/hr = tanθ θ = 7.5° North of East

a 2 + b 2 = c 2 tan θ = opp/adj (typically used to find the angle) cos θ = adj/hyp (typically used...

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