Projectile motion refers to the trajectory of objects through the air without propulsion. It has independent horizontal and vertical motions, with the horizontal motion being uniform and the vertical motion being accelerated downward by gravity. The trajectory of a projectile forms a parabolic curve. Key equations given relate the total time, horizontal range, and maximum height of a projectile to its initial velocity and launch angle. The horizontal range is greatest when the launch angle is 45 degrees.
Examinee's Guide in Taking CSE-PPT (Ballpen-based)John Homer Alim
Important reminders in taking Career Service Examination - Pen and Paper Test (CSE-PPT) Ballpen-based. The guide covers from the school and room assignment to the reminders on the day of examination. Also included are the 'Anti-Cheating Law' and the 'CSC Social Responsibility Program'.
Location:
Absolute Location:
-Between 17˚ 48’ and 18˚ 29’ north latitudes
-120˚ 5’ and 120˚ 58’ east longitudes
Relative Location:
- Ilocos Norte located at the northwest corner of Luzon Island
- 487 kilometers north-northwest of Manila.
-By air: 48 minutes from Manila; 80 minutes from Taipei -By land: 9 hours from Manila; 5 hours from Baguio
Laoag is the capital city
Population: 568,017 as of 2010
PHYSICAL CHARACTERISTICS:
land area: 3,467.89 km2
Seasons:
Dry - November to April
Wet - May to October
physical features: hills, mountains, coastal and miscellaneous land types. Its terrain is generally mountainous and rocky. There are thirteen (13) mountains in the area
Based on (NSCB) and Human Development Network, Ilocos Norte had the highest Human Development Index (HDI) among the four provinces of Region I.
Bain is the Ilocano trait for hiya or amor propio (sence of shame).
It is essentially to show panagdayaw (respect for the sensitivities of others).
They also celebrate fiestas like:
Pamulinawen Festival, Laoag City, February 10
Guling-Guling Festival, Paoay, Eve of Ash Wednesday
December Festival, Laoag City
Farmer’s Festival, Bacarra
Magdadaran: Talip Festival, Adams & Carassi
Language: Ilocano (Iloko), Filipino and English
Political Subdivisions:
One city
22 municipalities and
557 baranggays
this province was similar to its neighbor by languages, industries, traditions and climate.
Examinee's Guide in Taking CSE-PPT (Ballpen-based)John Homer Alim
Important reminders in taking Career Service Examination - Pen and Paper Test (CSE-PPT) Ballpen-based. The guide covers from the school and room assignment to the reminders on the day of examination. Also included are the 'Anti-Cheating Law' and the 'CSC Social Responsibility Program'.
Location:
Absolute Location:
-Between 17˚ 48’ and 18˚ 29’ north latitudes
-120˚ 5’ and 120˚ 58’ east longitudes
Relative Location:
- Ilocos Norte located at the northwest corner of Luzon Island
- 487 kilometers north-northwest of Manila.
-By air: 48 minutes from Manila; 80 minutes from Taipei -By land: 9 hours from Manila; 5 hours from Baguio
Laoag is the capital city
Population: 568,017 as of 2010
PHYSICAL CHARACTERISTICS:
land area: 3,467.89 km2
Seasons:
Dry - November to April
Wet - May to October
physical features: hills, mountains, coastal and miscellaneous land types. Its terrain is generally mountainous and rocky. There are thirteen (13) mountains in the area
Based on (NSCB) and Human Development Network, Ilocos Norte had the highest Human Development Index (HDI) among the four provinces of Region I.
Bain is the Ilocano trait for hiya or amor propio (sence of shame).
It is essentially to show panagdayaw (respect for the sensitivities of others).
They also celebrate fiestas like:
Pamulinawen Festival, Laoag City, February 10
Guling-Guling Festival, Paoay, Eve of Ash Wednesday
December Festival, Laoag City
Farmer’s Festival, Bacarra
Magdadaran: Talip Festival, Adams & Carassi
Language: Ilocano (Iloko), Filipino and English
Political Subdivisions:
One city
22 municipalities and
557 baranggays
this province was similar to its neighbor by languages, industries, traditions and climate.
EASTERN MINDANAO'S HISTORY, GEOGRAPHY, CULTURE AND TOURISM
PS: It is mindanao not visayas *If you want the Ms Powerpoint Presentation of it just email me at gepfelaire@gmail.com
MIMAROPA is an administrative region in the Philippines, designated as Region IV-B. It is one of two regions in the country having no land border with another region, the other being Eastern Visayas. The name is an acronym combination of its constituent provinces, which are: Mindoro (divided into Occidental Mindoro and Oriental Mindoro), Marinduque, Romblon and Palawan. The region is also formally known as the Southern Tagalog Islands.
Calapan City is the regional center. However, most regional government offices such as the Department of Public Works and Highways are in the city of Quezon in Metro Manila.
The region was part of the now-defunct Southern Tagalog region until May 17, 2002.[4] On May 23, 2005, Palawan and the highly urbanized city of Puerto Princesa were moved to the region of Western Visayas by Executive Order No. 429.
However, on August 19, 2005, then-President Arroyo issued Administrative Order No. 129 to hold the earlier EO 429 in abeyance pending a review.
Northern and Central Luzon: Its Physical and Cultural CharacteristicsJameson Bayan
This presents the physical features, as well as the cultural characteristics of the regions in northern and central Luzon namely CAR, Ilocos Region, Cagayan Valley and Central Luzon.
Cagayan Valley also known as "Land of beauty". It has plentiful of natural resources. It conveys different development potentials
with an area of 26,858 square kilometers.
EASTERN MINDANAO'S HISTORY, GEOGRAPHY, CULTURE AND TOURISM
PS: It is mindanao not visayas *If you want the Ms Powerpoint Presentation of it just email me at gepfelaire@gmail.com
MIMAROPA is an administrative region in the Philippines, designated as Region IV-B. It is one of two regions in the country having no land border with another region, the other being Eastern Visayas. The name is an acronym combination of its constituent provinces, which are: Mindoro (divided into Occidental Mindoro and Oriental Mindoro), Marinduque, Romblon and Palawan. The region is also formally known as the Southern Tagalog Islands.
Calapan City is the regional center. However, most regional government offices such as the Department of Public Works and Highways are in the city of Quezon in Metro Manila.
The region was part of the now-defunct Southern Tagalog region until May 17, 2002.[4] On May 23, 2005, Palawan and the highly urbanized city of Puerto Princesa were moved to the region of Western Visayas by Executive Order No. 429.
However, on August 19, 2005, then-President Arroyo issued Administrative Order No. 129 to hold the earlier EO 429 in abeyance pending a review.
Northern and Central Luzon: Its Physical and Cultural CharacteristicsJameson Bayan
This presents the physical features, as well as the cultural characteristics of the regions in northern and central Luzon namely CAR, Ilocos Region, Cagayan Valley and Central Luzon.
Cagayan Valley also known as "Land of beauty". It has plentiful of natural resources. It conveys different development potentials
with an area of 26,858 square kilometers.
This presentation by Morris Kleiner (University of Minnesota), was made during the discussion “Competition and Regulation in Professions and Occupations” held at the Working Party No. 2 on Competition and Regulation on 10 June 2024. More papers and presentations on the topic can be found out at oe.cd/crps.
This presentation was uploaded with the author’s consent.
Acorn Recovery: Restore IT infra within minutesIP ServerOne
Introducing Acorn Recovery as a Service, a simple, fast, and secure managed disaster recovery (DRaaS) by IP ServerOne. A DR solution that helps restore your IT infra within minutes.
Have you ever wondered how search works while visiting an e-commerce site, internal website, or searching through other types of online resources? Look no further than this informative session on the ways that taxonomies help end-users navigate the internet! Hear from taxonomists and other information professionals who have first-hand experience creating and working with taxonomies that aid in navigation, search, and discovery across a range of disciplines.
Sharpen existing tools or get a new toolbox? Contemporary cluster initiatives...Orkestra
UIIN Conference, Madrid, 27-29 May 2024
James Wilson, Orkestra and Deusto Business School
Emily Wise, Lund University
Madeline Smith, The Glasgow School of Art
This presentation, created by Syed Faiz ul Hassan, explores the profound influence of media on public perception and behavior. It delves into the evolution of media from oral traditions to modern digital and social media platforms. Key topics include the role of media in information propagation, socialization, crisis awareness, globalization, and education. The presentation also examines media influence through agenda setting, propaganda, and manipulative techniques used by advertisers and marketers. Furthermore, it highlights the impact of surveillance enabled by media technologies on personal behavior and preferences. Through this comprehensive overview, the presentation aims to shed light on how media shapes collective consciousness and public opinion.
0x01 - Newton's Third Law: Static vs. Dynamic AbusersOWASP Beja
f you offer a service on the web, odds are that someone will abuse it. Be it an API, a SaaS, a PaaS, or even a static website, someone somewhere will try to figure out a way to use it to their own needs. In this talk we'll compare measures that are effective against static attackers and how to battle a dynamic attacker who adapts to your counter-measures.
About the Speaker
===============
Diogo Sousa, Engineering Manager @ Canonical
An opinionated individual with an interest in cryptography and its intersection with secure software development.
9. x
y
•Motion is accelerated
•Acceleration is constant,
and downward
• a = g = -9.81m/s2
•The horizontal (x)
component of velocity is
constant
•The horizontal and
vertical motions are
independent of each other,
but they have a common
time
g = -9.81m/s2
10. ANALYSIS OF MOTION
ASSUMPTIONS:
• x-direction (horizontal): uniform motion
• y-direction (vertical): accelerated motion
• no air resistance
QUESTIONS:
• What is the trajectory?
• What is the total time of the motion?
• What is the horizontal range?
• What is the final velocity?
11. x
y
0
Frame of reference:
h
v0
Equations of motion:
X
Uniform m.
Y
Accel. m.
ACCL. ax = 0 ay = g = -9.81
m/s2
VELC. vx = v0 vy = g t
DSPL. x = v0 t y = h + ½ g t2
g
12. Trajectory
x = v0 t
y = h + ½ g t2
Eliminate time, t
t = x/v0
y = h + ½ g (x/v0)2
y = h + ½ (g/v0
2
) x2
y = ½ (g/v0
2
) x2
+ h
y
x
h
Parabola, open down
v01
v02 > v01
13. Total Time, Δt
y = h + ½ g t2
final y = 0 y
x
h
ti =0
tf =Δt
0 = h + ½ g (Δt)2
Solve for Δt:
Δt = √ 2h/(-g)
Δt = √ 2h/(9.81ms-2
)
Total time of motion depends
only on the initial height, h
Δt = tf - ti
14. Horizontal Range, Δx
final y = 0, time is
the total time Δt
y
x
h
Δt = √ 2h/(-g)
Δx = v0 √ 2h/(-g)
Horizontal range depends on the
initial height, h, and the initial
velocity, v0
Δx
x = v0 t
Δx = v0 Δt
15. VELOCITY
v
vx = v0
vy = g t
v = √vx
2
+ vy
2
= √v0
2
+g2
t2
tg Θ = v / v = g t / v
Θ
16. FINAL VELOCITY
v
vx = v0
vy = g t
v = √vx
2
+ vy
2
v = √v0
2
+g2
(2h /(-g))
v = √ v0
2
+ 2h(-g)
Θ
tg Θ = g Δt / v0
= -(-g)√2h/(-g) / v0
= -√2h(-g) / v0
Θ is negative
(below the
horizontal line)
Δt = √ 2h/(-g)
17. HORIZONTAL THROW - Summary
Trajectory Half -parabola, open
down
Total time Δt = √ 2h/(-g)
Horizontal Range Δx = v0 √ 2h/(-g)
Final Velocity v = √ v0
2
+ 2h(-g)
tg Θ = -√2h(-g) / v0
h – initial height, v0 – initial horizontal velocity, g = -9.81m/s2
19. vi
x
y
θ
vix
viy
Initial velocity: vi = vi [Θ]
Velocity components:
x- direction : vix = vi cos Θ
y- direction : viy = vi sin Θ
Initial position: x = 0, y = 0
20. x
y
• Motion is accelerated
• Acceleration is constant, and
downward
• a = g = -9.81m/s2
• The horizontal (x) component of
velocity is constant
• The horizontal and vertical
motions are independent of each
other, but they have a common
time
a = g =
- 9.81m/s2
21. ANALYSIS OF MOTION:
ASSUMPTIONS
• x-direction (horizontal): uniform motion
• y-direction (vertical): accelerated motion
• no air resistance
QUESTIONS
• What is the trajectory?
• What is the total time of the motion?
• What is the horizontal range?
• What is the maximum height?
• What is the final velocity?
22. Equations of motion:
X
Uniform motion
Y
Accelerated motion
ACCELERATION ax = 0 ay = g = -9.81 m/s2
VELOCITY vx = vix= vi cos Θ
vx = vi cos Θ
vy = viy+ g t
vy = vi sin Θ + g t
DISPLACEMENT x = vix t = vi t cos Θ
x = vi t cos Θ
y = h + viy t + ½ g t2
y = vi tsin Θ + ½ g t2
23. Equations of motion:
X
Uniform motion
Y
Accelerated motion
ACCELERATION ax = 0 ay = g = -9.81 m/s2
VELOCITY vx = vi cos Θ vy = vi sin Θ + g t
DISPLACEMENT x = vi t cos Θ y = vi tsin Θ + ½ g t2
24. Trajectory
x = vi t cos Θ
y = vi tsin Θ + ½ g t2
Eliminate time, t
t = x/(vi cos Θ)
y
x
Parabola, open down
2
22
22
2
cos2
tan
cos2cos
sin
x
v
g
xy
v
gx
v
xv
y
i
ii
i
Θ
+Θ=
Θ
+
Θ
Θ
=
y = bx + ax2
25. Total Time, Δt
final height y = 0, after time interval Δt
0 = vi Δtsin Θ + ½ g (Δt)2
Solve for Δt:
y = vi tsin Θ + ½ g t2
0 = vi sin Θ + ½ g Δt
Δt =
2 vi sin Θ
(-g)
t = 0 Δt
x
26. Horizontal Range, Δx
final y = 0, time is
the total time Δt
x = vi t cos Θ
Δx = vi Δt cos Θ
x
Δx
y
0
Δt =
2 vi sin Θ
(-g)
Δx =
2vi
2
sin Θ cos Θ
(-g)
Δx =
vi
2
sin (2 Θ)
(-g)
sin (2 Θ) = 2 sin Θ cos Θ
27. Horizontal Range, Δx
Δx =
vi
2
sin (2 Θ)
(-g)
Θ (deg) sin (2Θ)
0 0.00
15 0.50
30 0.87
45 1.00
60 0.87
75 0.50
90 0
•CONCLUSIONS:
•Horizontal range is greatest for the
throw angle of 450
• Horizontal ranges are the same for
angles Θ and (900
– Θ)
28. Trajectory and horizontal range
2
22
cos2
tan x
v
g
xy
i Θ
+Θ=
0
5
10
15
20
25
30
35
0 20 40 60 80
15 deg
30 deg
45 deg
60 deg
75 deg
vi = 25 m/s
29. Velocity
•Final speed = initial speed (conservation of energy)
•Impact angle = - launch angle (symmetry of parabola)
30. Maximum Height
vy = vi sin Θ + g t
y = vi tsin Θ + ½ g t2
At maximum height vy = 0
0 = vi sin Θ + g tup
tup =
vi sin Θ
(-g)
tup = Δt/2
hmax = vi tupsin Θ + ½ g tup
2
hmax = vi
2
sin2
Θ/(-g) + ½ g(vi
2
sin2
Θ)/g2
hmax =
vi
2
sin2
Θ
2(-g)
31. Projectile Motion – Final Equations
Trajectory Parabola, open down
Total time Δt =
Horizontal range Δx =
Max height hmax =
(0,0) – initial position, vi = vi [Θ]– initial velocity, g = -9.81m/s2
2 vi sin Θ
(-g)
vi
2
sin (2 Θ)
(-g)
vi
2
sin2
Θ
2(-g)
32. PROJECTILE MOTION - SUMMARY
Projectile motion is motion with a constant
horizontal velocity combined with a constant
vertical acceleration
The projectile moves along a parabola