The Sinking Ship You again are on duty at Coast Guard HQ when you get a distress call from a...
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Transcript of The Sinking Ship You again are on duty at Coast Guard HQ when you get a distress call from a...
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
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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?