The Sinking ShipThe Sinking Ship You again are on duty at Coast Guard HQ

when you get a distress call from a sinking ship. Your radar station locates the ship at range 17.3km and bearing 136° clockwise from north. You also locate a rescue boat 19.6km 153° clockwise from north. You need to radio to the captain of the rescue ship the distance and course (direction) needed to travel in order to rescue the members of the sinking ship.

The Sinking ShipThe Sinking Ship

ProjectProject Walk in one direction, then stop and walk Walk in one direction, then stop and walk

in a 90° different direction.in a 90° different direction. Have someone measure your distance Have someone measure your distance

traveled in each direction and total traveled in each direction and total displacement traveled.displacement traveled.

Record all your measurements.Record all your measurements.

Distance 1Distance 1 Distance 2Distance 2 DisplacemenDisplacementt

Lesson #13Lesson #13Topic: Topic: Drawing and Adding VectorsObjectives: Objectives: (After this class I will be able to)(After this class I will be able to)

1.1. Split diagonal vectors up into (x) and Split diagonal vectors up into (x) and (y) components(y) components

2.2. Find the magnitude of a resultant Find the magnitude of a resultant vector given the x and y components vector given the x and y components of that vectorof that vector

10/3/06

Assignment: “Adding Vectors” due tomorrow

Warm Up: Your flight takes off in Pittsburg and flies with a constant speed of 350 km/h towards Chicago which is 600km away. The plane experiences a 50 km/h headwind throughout the entire trip. How long does it take you to get to Chicago?

Your flight takes off in Pittsburgh and flies with a constant speed of 350 km/h towards Chicago which is 600km away. The plane

experiences a 50 km/h headwind throughout the entire trip. How long does it take you to

get to Chicago?1.1. 1.71 hours1.71 hours2.2. 12 hours12 hours3.3. 2 hours2 hours4.4. 1.5 hours1.5 hours

Drawing and Adding Drawing and Adding VectorsVectors Only vectors with the same units can be Only vectors with the same units can be

added.added. Vector Diagrams are used to assist in Vector Diagrams are used to assist in

combining vectors.combining vectors. Vectors are represented with arrows to Vectors are represented with arrows to

show their direction.show their direction. Vectors in the same or opposite direction Vectors in the same or opposite direction

can be simply added or subtracted.can be simply added or subtracted. Vectors perpendicular to one another Vectors perpendicular to one another

must be combined using Pythagorean must be combined using Pythagorean Theorem. Theorem.

Drawing and Adding Drawing and Adding VectorsVectors Horizontal and vertical pieces are Horizontal and vertical pieces are

components components of an overall of an overall resultantresultant vector.vector.

Component Vectors are drawn Component Vectors are drawn completely in the x or y direction.completely in the x or y direction.

Resultant vectors are drawn from the Resultant vectors are drawn from the tail of the first component to the head tail of the first component to the head of the last component.of the last component.

x component

y component

Resultant y

component

x component

Which of the following Which of the following statements is statements is FalseFalse??

Vectors

are re

presen

t..

Vectors

in opposit

e d...

Vectors

perpen

dicula.

..

Two or m

ore co

mpon...

0% 0%0%0%

1.1. Vectors are represented Vectors are represented with arrows.with arrows.

2.2. Vectors in opposite Vectors in opposite directions are directions are subtracted from one subtracted from one another.another.

3.3. Vectors perpendicular Vectors perpendicular to one another are to one another are added.added.

4.4. Two or more Two or more componentscomponents make up make up a a resultantresultant vector vector

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Vector diagrams:Vector diagrams: Example 1: A dog walks 20m east, Example 1: A dog walks 20m east,

stops and then walks 10 more meters stops and then walks 10 more meters east. What is the dog’s displacement? east. What is the dog’s displacement?

Example 2: A dog walks 40m east, Example 2: A dog walks 40m east, stops and then walks 10 m west. stops and then walks 10 m west. What is the dog’s displacement? What is the dog’s displacement?

Example 3: A dog walks 40m east, stops Example 3: A dog walks 40m east, stops and then walks 30 more meters north. and then walks 30 more meters north.

What is the dog’s displacement? What is the dog’s displacement?

45m N

orthea

st

70m N

orthea

st

10m N

orthea

st

50m N

orthea

st

0% 0%0%0%

1.1. 45m Northeast45m Northeast2.2. 70m Northeast70m Northeast3.3. 10m Northeast10m Northeast4.4. 50m Northeast50m Northeast

0of5

Which of the following is Which of the following is truetrue??

Only

vecto

rs with

th...

Vectors

in the s

ame d

...

Vectors

in opposit

e d...

Vectors

not in

the s

...

All of th

ese

0% 0% 0%0%0%

1.1. Only vectors with the Only vectors with the same units can be added.same units can be added.

2.2. Vectors in the same Vectors in the same direction are simply direction are simply added.added.

3.3. Vectors in opposite Vectors in opposite directions are subtracted.directions are subtracted.

4.4. Vectors not in the same or Vectors not in the same or opposite directions need a opposite directions need a triangular vector diagram.triangular vector diagram.

5.5. All of theseAll of these

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Parallelogram ruleParallelogram rule Use the parallelogram rule to draw Use the parallelogram rule to draw

the resultant vectors for the the resultant vectors for the following diagrams.following diagrams.

Lesson #14Lesson #14Topic: Topic: TrigonometryObjectives: Objectives: (After this class I will be able to)(After this class I will be able to)

1.1. Use trig functions and angles to Use trig functions and angles to find an unknown side of a find an unknown side of a triangle.triangle.

2.2. Label unknowns with appropriate Label unknowns with appropriate variablesvariables

10/1/07

Assignment: “SOH CAH TOA” due tomorrow“Angles and Vectors” due Wed

Project: Walk a few meters towards 45° NE. Have a partner measure your displacement. How far East did you walk? How far North did you walk?

TrigonometryTrigonometry Solving for unknowns using right Solving for unknowns using right

trianglestriangles If you know 2 sides of a right triangle If you know 2 sides of a right triangle

you can solve to find the unknown side you can solve to find the unknown side and the unknown anglesand the unknown angles

If you know a side of a right triangle If you know a side of a right triangle and an angle you can find the other 2 and an angle you can find the other 2 unknown sidesunknown sides

Trig functions can be found on any Trig functions can be found on any scientific calculator (which you scientific calculator (which you definitely need to have).definitely need to have).

SOH CAH TOASOH CAH TOA Sine, Cosine, and Tangent are the ratios Sine, Cosine, and Tangent are the ratios

of the lengths of two sides of a right of the lengths of two sides of a right triangle for any given angle. triangle for any given angle.

You tell the calculator the angle, it tells You tell the calculator the angle, it tells you the appropriate ratio.you the appropriate ratio.

θθ = = variable for an anglevariable for an angle Works only for right trianglesWorks only for right triangles sin (23°) does sin (23°) does notnot mean sin * 23 mean sin * 23 sin, cos, and tan are a new type of sin, cos, and tan are a new type of

function function

You can solve for a side of a You can solve for a side of a right triangle if…right triangle if…

You know

the o

ther

t..

You know

a sid

e and .

.

You know

every

angl... 1&

2

1,2,&

3

0% 0% 0%0%0%

1.1. You know the You know the other two sidesother two sides

2.2. You know a side You know a side and an angle and an angle (besides the 90°)(besides the 90°)

3.3. You know every You know every angle but no sidesangle but no sides

4.4. 1&21&25.5. 1,2,&31,2,&3

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SOH CAH TOASOH CAH TOA SOH – SOH – ssin in θθ = = OOpposite side / pposite side /

HHypotenuseypotenuse CAH – CAH – ccos os θθ = = AAdjacent side / djacent side /

HHypotenuseypotenuse TOA – TOA – ttan an θθ = = OOpposite side / pposite side /

AAdjacent sidedjacent side

53)8.36sin(

54)8.36cos(

43)8.36tan(

Example:

3

4

5

36.8°

Practice ProblemPractice ProblemJoe walks 6km at 30° North of East. Create

a vector diagram of Joe’s path and draw and label the x and y components of his displacement.

How far east did Joe travel?How far east did Joe travel? How far north did Joe travel?How far north did Joe travel?

d = 6km

θ = 30°

dx = ?

dy

= ?

Practice ProblemPractice Problem

θ = 25°

Trig PracticeTrig Practice

25°

75°

60°

40°

d=50m

dx=10m

v =70m/s

vy=20m/s

dx=?

vx=?

vx=?

vy=?

dy=? dy=?

v=?

d=?

Practice ProblemsPractice Problems1. Steve sails his boat with a velocity of 1. Steve sails his boat with a velocity of

15m/s at 40° S of W. 15m/s at 40° S of W. Solve for the south and west Solve for the south and west components of his velocity.components of his velocity.

2. A cannon ball is fired with an initial 2. A cannon ball is fired with an initial velocity of 650m/s at a 40° angle above velocity of 650m/s at a 40° angle above the horizontal. What are the x and y the horizontal. What are the x and y components of the initial velocity? components of the initial velocity?

Practice ProblemsPractice Problems3.3. Sarah is flying her airplane 60° East of Sarah is flying her airplane 60° East of

South. The wind is blowing 12m/s toward South. The wind is blowing 12m/s toward the East. What is the speed of Sarah’s the East. What is the speed of Sarah’s airplane?airplane?

4.4. Frank goes for a jog. He heads in a Frank goes for a jog. He heads in a direction 40° East of North. After 3 direction 40° East of North. After 3 minutes he is 400m North of where he minutes he is 400m North of where he began. What is Frank’s began. What is Frank’s speed? How far East speed? How far East has he traveled? has he traveled?

The adjacent side of a 30° The adjacent side of a 30° angle of a right triangle is angle of a right triangle is

10. What is the 10. What is the hypotenuse?hypotenuse?

10/co

s30°

(cos

30°)/

10

10co

s30°

10/si

n30°

10sin

30°

0% 0% 0%0%0%

1.1. 10/cos30°10/cos30°2.2. (cos30°)/10(cos30°)/103.3. 10cos30°10cos30°4.4. 10/sin30°10/sin30°5.5. 10sin30°10sin30°

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The hypotenuse of a 30° The hypotenuse of a 30° angle of a right triangle is angle of a right triangle is 25. What is the opposite 25. What is the opposite

side?side?

0 of 5 25

/cos3

0°

(tan30

°)/25

25sin

30°

25/si

n30°

25co

s30°

0% 0% 0%0%0%

1.1. 25/cos30°25/cos30°2.2. (tan30°)/25(tan30°)/253.3. 25sin30°25sin30°4.4. 25/sin30°25/sin30°5.5. 25cos30°25cos30°

Lesson #15Lesson #15Topic: Topic: Vectors and AnglesObjectives: Objectives: (After this class I will be able to)(After this class I will be able to)

1.1. Solve for an unknown angle given Solve for an unknown angle given two components of a right triangle.two components of a right triangle.

10/5/07

Assignment: New Wikispaces postExam 2 Review Due tuesday!

Warm Up: Jane walks at 60° North of East with a speed of 2m/s for 5 minutes. Create a vector diagram of Jane’s path and solve for the x and y components of her displacement.

Jane walks at 60° North of East with a speed of 2m/s for 5 minutes. Create a vector diagram of

Jane’s path and solve for the x and y components of her displacement.

x=30

0m, y

=520m

x=52

0m, y

=300m

x=8.6

6m, y

=5m

x=5m

, y

=8.66m

0% 0%0%0%

1.1. x=300m, x=300m, y=520my=520m

2.2. x=520m, x=520m, y=300my=300m

3.3. x=8.66m, x=8.66m, y=5my=5m

4.4. x=5m, x=5m, y=8.66my=8.66m

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Inverse Trig FunctionsInverse Trig Functions When solving for an unknown angle you must When solving for an unknown angle you must

do the opposite of taking the sin, cos, or tan of do the opposite of taking the sin, cos, or tan of an angle.an angle.

The opposite of these functions are sinThe opposite of these functions are sin-1-1, cos, cos-1-1, , tantan-1-1

Example: Example: sinsinθθ = 3/5 then = 3/5 then θθ = = sinsin-1-1(3/5) so (3/5) so θθ = 36.8° = 36.8°

The same rules apply for cosine and tangent.The same rules apply for cosine and tangent.

Trig PracticeTrig Practice

θ

d=50m

dx=10m

v =70m/s

vy=20m/s

dx=?

vx=?

vx=15m/s

vy=35m/s

dx=25 dy=25

v=?

d=?

θ

θ

θ

Practice ProblemPractice Problem Joe walks 60m east and then 80m Joe walks 60m east and then 80m

north. Find the magnitude and north. Find the magnitude and directiondirection of Joe’s displacement. of Joe’s displacement.

Practice ProblemPractice Problem A boat is motoring from the west side A boat is motoring from the west side

to the east side of a river. The to the east side of a river. The velocity of the boat is 17m/s. The velocity of the boat is 17m/s. The current of the river flows towards the current of the river flows towards the south with a speed of 8m/s. south with a speed of 8m/s.

In what direction is the boat In what direction is the boat traveling?traveling?

How fast would the boat move if the How fast would the boat move if the river were perfectly still? river were perfectly still?

Lesson #16Lesson #16Topic: Topic: Acceleration and Vector Exam ReviewObjectives: Objectives: (After this class I will be able to)(After this class I will be able to)

1.1. Practice solving physics problemsPractice solving physics problems2.2. Complete and check Exam 2 ReviewComplete and check Exam 2 Review3.3. Plan a tutoring time (if needed)Plan a tutoring time (if needed)4.4. Complete a bonus problem Complete a bonus problem

opportunityopportunity

10/8/07

Assignment: Exam 2 Review Due Wednesday!Study for Exam 2

Warm Up: Jim drives 9km West and then turns North and drives 12 km. Find the magnitude and direction of Jim’s displacement.

Jim drives 9km West and then turns North and drives 12 km. Find the magnitude and direction of Jim’s

displacement.

15km

36.9°

N of W

15km

53.1°

N of W

225k

m 36.9°

N of W

225k

m 53.1°

N of

W

0% 0%0%

100%1.1. 15km 36.9° N 15km 36.9° N

of Wof W2.2. 15km 53.1° N 15km 53.1° N

of Wof W3.3. 225km 36.9° N 225km 36.9° N

of Wof W4.4. 225km 53.1° N 225km 53.1° N

of Wof W

ConceptsConcepts What is gravity?What is gravity?

What does gravity depend on?What does gravity depend on?

What can you say about two objects What can you say about two objects released at the same time?released at the same time?

What is an example of vertical What is an example of vertical acceleration?acceleration?

What is an example of non-vertical What is an example of non-vertical acceleration?acceleration?

A river boat is traveling upstream A river boat is traveling upstream with a speed of 3m/s. The river with a speed of 3m/s. The river has a current of 2m/s. How fast has a current of 2m/s. How fast

would the boat move on still would the boat move on still water?water?

1m/s

3m/s

5m/s

7m/s

10%0%

80%

10%

1.1. 1m/s1m/s2.2. 3m/s3m/s3.3. 5m/s5m/s4.4. 7m/s7m/s

A river boat is traveling upstream A river boat is traveling upstream with a speed of 3m/s. The river with a speed of 3m/s. The river has a current of 2m/s. How fast has a current of 2m/s. How fast

would the boat move downstream?would the boat move downstream?

1m/s

3m/s

5m/s

7m/s

0%

100%

0%0%

1.1. 1m/s1m/s2.2. 3m/s3m/s3.3. 5m/s5m/s4.4. 7m/s7m/s

Gravity practiceGravity practice A stone is thrown vertically upward A stone is thrown vertically upward

with an initial velocity of 18m/s.with an initial velocity of 18m/s. How long is the stone in the air?How long is the stone in the air? How high does the stone go above How high does the stone go above

the ground?the ground? Make a velocity vs. time graph of the Make a velocity vs. time graph of the

stone’s motion.stone’s motion.

Bonus 2pts eachBonus 2pts each1.1. Eli finds a map for a buried treasure. It Eli finds a map for a buried treasure. It

tells him to begin at the old oak and walk tells him to begin at the old oak and walk 21 paces due west, 41 paces and an angle 21 paces due west, 41 paces and an angle 45° south of west, 69 paces due north, 20 45° south of west, 69 paces due north, 20 paces dues east, and 50 paces at an angle paces dues east, and 50 paces at an angle of 53° south of east. How far and what of 53° south of east. How far and what direction from the oak tree is the buried direction from the oak tree is the buried treasure? treasure?

2.2. Veronica can swim 3m/s in still water. Veronica can swim 3m/s in still water. While trying to swim directly across a river While trying to swim directly across a river from west to east, Veronica is pulled by a from west to east, Veronica is pulled by a current flowing southward at 2m/s. What is current flowing southward at 2m/s. What is the magnitude of her resultant velocity? If the magnitude of her resultant velocity? If she wants to end up directly across stream she wants to end up directly across stream from where she began, at what angle to the from where she began, at what angle to the shore must she swim upstream? shore must she swim upstream?