3.2 vector operations
DESCRIPTION
3.2 Vector Operations. Review. Find the x and y component. Go 4 m to the right, 2 m up, 5 m down, 7m left, 3m to the left and 10 m up. X= 6m left y = 7m up. Pythagorean’s Theorem. c 2 = a 2 + b 2 c - PowerPoint PPT PresentationTRANSCRIPT
![Page 1: 3.2 Vector Operations](https://reader033.vdocuments.site/reader033/viewer/2022061504/56815b13550346895dc8c325/html5/thumbnails/1.jpg)
3.2 Vector Operations
![Page 2: 3.2 Vector Operations](https://reader033.vdocuments.site/reader033/viewer/2022061504/56815b13550346895dc8c325/html5/thumbnails/2.jpg)
ReviewFind the x and y component.
Go 4 m to the right, 2 m up, 5 m down, 7m left, 3m to the left and 10 m up.
X= 6m left y = 7m up
![Page 3: 3.2 Vector Operations](https://reader033.vdocuments.site/reader033/viewer/2022061504/56815b13550346895dc8c325/html5/thumbnails/3.jpg)
Pythagorean’s Theorem
c2 = a2 + b2
c a
b
![Page 4: 3.2 Vector Operations](https://reader033.vdocuments.site/reader033/viewer/2022061504/56815b13550346895dc8c325/html5/thumbnails/4.jpg)
SOH CAH TOA
• Sin = opposite hypotenuse
• Cos = adjacent hypotenuse
• Tan = oppositeadjacent
![Page 5: 3.2 Vector Operations](https://reader033.vdocuments.site/reader033/viewer/2022061504/56815b13550346895dc8c325/html5/thumbnails/5.jpg)
Head to Tail Method
![Page 6: 3.2 Vector Operations](https://reader033.vdocuments.site/reader033/viewer/2022061504/56815b13550346895dc8c325/html5/thumbnails/6.jpg)
Helpful Hints to Solving Vector Problems
1. Place a dot on your paper
2. Draw the first vector given in the problem in the appropriate direction.
3. Without picking your pencil point off the paper draw the next vector in the appropriate direction.
4. Continue this with as many vectors as you have.
![Page 7: 3.2 Vector Operations](https://reader033.vdocuments.site/reader033/viewer/2022061504/56815b13550346895dc8c325/html5/thumbnails/7.jpg)
Helpful Hints to Solving Vector Problems
5. Draw your resultant from the dot in the beginning to the last vector arrow
6. Look at your drawing. You need to make a right triangle opposite your resultant.
7. Use pythagorean’s theorem to find the resultant side c
8. Vectors must have direction so you will use tan to find the angle from the resultant to the vector. (This angle always rotates around the original dot)
![Page 8: 3.2 Vector Operations](https://reader033.vdocuments.site/reader033/viewer/2022061504/56815b13550346895dc8c325/html5/thumbnails/8.jpg)
Direction
N
W E
S
![Page 9: 3.2 Vector Operations](https://reader033.vdocuments.site/reader033/viewer/2022061504/56815b13550346895dc8c325/html5/thumbnails/9.jpg)
A plane travels from Huston, Texas to Washington, DC, which is 1540 km, East and 1160km north of Houston. What is the total displacement of the plane?
C 1160 KM
1540 km
![Page 10: 3.2 Vector Operations](https://reader033.vdocuments.site/reader033/viewer/2022061504/56815b13550346895dc8c325/html5/thumbnails/10.jpg)
c2 = a2 + b2
c2 = (1540 km)2 + (1160km)2
C = 1928 km = 1930 km
Tan = 1160
1540
Answer: 1930 km, north of east Practice: 90 degree Problems
![Page 11: 3.2 Vector Operations](https://reader033.vdocuments.site/reader033/viewer/2022061504/56815b13550346895dc8c325/html5/thumbnails/11.jpg)
![Page 12: 3.2 Vector Operations](https://reader033.vdocuments.site/reader033/viewer/2022061504/56815b13550346895dc8c325/html5/thumbnails/12.jpg)
Boat Problems
A motorboat heads due east at 16 m /s across a river that flows due south at 9.0 m /s.
A. What Is the resultant velocity of the boat.
B. If the river is 136 m wide, how long does it take the motorboat to reach the other side?
C. How far downstream is the boat when it reaches the other side of the river?
![Page 13: 3.2 Vector Operations](https://reader033.vdocuments.site/reader033/viewer/2022061504/56815b13550346895dc8c325/html5/thumbnails/13.jpg)
What Is the resultant velocity of the
boat? 16 m /s
c 9 m /s
C 2 = (16)2 + (9)2 C = 18 m /s
Tan 9 / 16 = 30o
18 m /s, 30o south of east
![Page 14: 3.2 Vector Operations](https://reader033.vdocuments.site/reader033/viewer/2022061504/56815b13550346895dc8c325/html5/thumbnails/14.jpg)
If the river is 136 m wide, how long does it take the motorboat to reach
the other side?
V = d t
t = d = 136 m V 16 m /s
t = 8.50 s
![Page 15: 3.2 Vector Operations](https://reader033.vdocuments.site/reader033/viewer/2022061504/56815b13550346895dc8c325/html5/thumbnails/15.jpg)
How far downstream is the boat when it reaches the other side of the river?
V = d
t
d = V t
d = 9.0 m /s X 8.5 s = 77 m
Practice: Boat problems
![Page 16: 3.2 Vector Operations](https://reader033.vdocuments.site/reader033/viewer/2022061504/56815b13550346895dc8c325/html5/thumbnails/16.jpg)
Components
You are given the resultant (magnitude and direction) and you find the sides or components
Use sin and cos to find the x and y component
Hypotenuse angle y
x
![Page 17: 3.2 Vector Operations](https://reader033.vdocuments.site/reader033/viewer/2022061504/56815b13550346895dc8c325/html5/thumbnails/17.jpg)
Component Example
An arrow is shot from a bow at an angle of 25o above the horizontal with an initial speed of 45 m /s. Find the horizontal and vertical components of the arrow’s initial velocity.
45 m /s
25o y X
![Page 18: 3.2 Vector Operations](https://reader033.vdocuments.site/reader033/viewer/2022061504/56815b13550346895dc8c325/html5/thumbnails/18.jpg)
Components
Sin 25o = y = 19 m /s 45
Cos 25o = x = 41 m /s 45
Practice problems on components
![Page 19: 3.2 Vector Operations](https://reader033.vdocuments.site/reader033/viewer/2022061504/56815b13550346895dc8c325/html5/thumbnails/19.jpg)
Putting it all together
A mouse runs east for 4 m across the living room, turns 30o north of east and runs 2.8 m and finally heads due north 3 m to a hole in the wall. What is the resultant?
3 m
2.8 m 30o
4 m
![Page 20: 3.2 Vector Operations](https://reader033.vdocuments.site/reader033/viewer/2022061504/56815b13550346895dc8c325/html5/thumbnails/20.jpg)
Draw and examine. Look for a right triangle. The resultant is “from where you start to where you end it does not
matter where you have been”. Find the components to make the right triangle.
3m C
q 1.4 m
4m 2.4 m
• Add up the all the x’s then all the y’s: x total = 6.4m y total = 4.4m• Use pythagorean’s theorem c 2 = a2 + b2 C = 7.8 m• tan = 4.4 / 6.4 = 35 o
7.8 m, 35 o North of East
![Page 21: 3.2 Vector Operations](https://reader033.vdocuments.site/reader033/viewer/2022061504/56815b13550346895dc8c325/html5/thumbnails/21.jpg)
A camper walks 4.5 km at 45o north of east then 4.5 km due south. Find the
campers total displacement.
4.5
45o 4.5
![Page 22: 3.2 Vector Operations](https://reader033.vdocuments.site/reader033/viewer/2022061504/56815b13550346895dc8c325/html5/thumbnails/22.jpg)
4.5 sin 45 = x x = 3.184.5 sin 45 = y1= 3.18
4.5 - 3.18 = 1.32c2 = 3.182 + 1.322 c = 3.4 tan = 1.32 / 3.18 = 22o
3.4 m, 22o south of east
4.5 45o 4.5
![Page 23: 3.2 Vector Operations](https://reader033.vdocuments.site/reader033/viewer/2022061504/56815b13550346895dc8c325/html5/thumbnails/23.jpg)
Practice, Practice, Practice
• Practice #1
• Practice #2
• Holt Text Pg 94 1-4
• QUIZ