FIRST ASIA INSTITUTE OF TECHNOLOGY AND HUMANITIES
Science, Technology, Engineering, and Mathematics
GENERAL PHYSICS
Performance Task
Submitted by:
Alexandra Herrera
(STEM12-A)
Submitted to:
Engr. Aeron Librada
(Physics Teacher)
October 30, 2020
INTRODUCTION:
It would be an odd sight indeed to watch a medieval-era cannon wheeled onto a
modern field of battle, with drones zooming about overhead and armored, motorized
tanks on the ground. However, not only was the cannon the most-feared mechanical
weapon in the world for a very long time, but the physical principles governing the form
of projectile motion embodied by a cannon ball also dictate those of modern guns. A
cannon has its own measurements. The diameter length of the cannon is 9 cm, height is
6cm and width is 5cm. The project is the representation of cannon and helps to easily
visualize it. Materials used in creating the project are cardboard (base, frame, and
wheel), popsicle stick (cannon), disc fragments (luminosity), balloon (mechanism),
crumpled paper (bullet) and paint (colors). Each measurement of the Cannon was
solved by the given Angle and Length of cannon (Hypotenuse) assigned by the
students. Finding the X and Y Components helps to find the sides of triangle by solving
it using Soh Cah Toa and checked it by using Pythagorean Theorem.
The figure is 3D, you can freely move it.
SIDE VIEW:
2 cm
6 cm
6.5 cm
BACK VIEW:
FRONT VIEW:
4 cm
3 cm
2 cm
4 cm
5 cm
4 cm
COMPUTATIONS:
h=9cm
X component
= 9cm
1. 𝟎°
Given: Angle = 0°
Length of cannon (Hypotenuse) = 9cm
Find: X & Y Components (sides of triangle)
Solution: Using Soh Cah Toa
X Component:
Y Component:
cos 0° =
𝑎𝑑𝑗
ℎ𝑦𝑝
sin 0° =
𝑜𝑝𝑝
ℎ𝑦𝑝
cos 0° =
𝑎𝑑𝑗
9𝑐𝑚
sin 0° =
𝑜𝑝𝑝
9𝑐𝑚
cos 0°(9𝑐𝑚) = 𝑎𝑑𝑗
sin 0°(9𝑐𝑚) = 𝑜𝑝𝑝
𝑎𝑑𝑗 = 9 𝑐𝑚
𝑜𝑝𝑝 = 0𝑐𝑚
Narrative interpretation:
Narrative interpretation:
To find the x component, use the
To find the y component, use the
𝑜𝑝𝑝
formula sin 0° =
, substitute the
formula cos 0° =
𝑎𝑑𝑗
ℎ𝑦𝑝
, substitute the
given to the formula and then, cross
multiply it to make the equation
cos 0°(9𝑐𝑚) = 𝑎𝑑𝑗. Simplify and
come up with the answer 𝑎𝑑𝑗 = 9 𝑐𝑚
ℎ𝑦𝑝
given to the formula and then, cross
multiply it to make the equation
sin 0°(9𝑐𝑚) = 𝑜𝑝𝑝. Simplify and
come up with the answer 𝑜𝑝𝑝 = 0𝑐𝑚
CHECKING:
Using Pythagorean theorem.
𝑐 = √𝑎 2 + 𝑏 2
𝑐 = √92 + 02
𝑐 = √81 + 0
𝑐 = 9 𝑐𝑚
Narrative interpretation:
To check the hypotenuse, use the
Pythagorean theorem formula
𝑐 = √𝑎2 + 𝑏 2 , substitute the given to the
formula. Simplify and come up with the
answer 𝑐 = 9 𝑐𝑚
x=
8.45cm
2. 𝟐𝟎°
Given: Angle = 20°
Length of cannon (Hypotenuse) = 9cm
Find: X & Y Components (sides of triangle)
Solution: Using Soh Cah Toa
X Component:
Y Component:
cos 20° =
𝑎𝑑𝑗
ℎ𝑦𝑝
sin 20° =
𝑜𝑝𝑝
ℎ𝑦𝑝
cos 20° =
𝑎𝑑𝑗
9𝑐𝑚
sin 20° =
𝑜𝑝𝑝
9𝑐𝑚
cos 20°(9𝑐𝑚) = 𝑎𝑑𝑗
𝑎𝑑𝑗 = 8.45 𝑐𝑚
sin 20°(9𝑐𝑚) = 𝑜𝑝𝑝
𝑜𝑝𝑝 = 3.07 𝑐𝑚
Narrative interpretation:
Narrative interpretation:
To find the x component, use the
To find the y component, use the
𝑜𝑝𝑝
formula sin 20° = ℎ𝑦𝑝, substitute the
𝑎𝑑𝑗
formula cos 20° = ℎ𝑦𝑝, substitute the
given to the formula and then, cross
multiply it to make the equation
cos 20°(9𝑐𝑚) = 𝑎𝑑𝑗. Simplify and come
up with the answer 𝑎𝑑𝑗 = 6.9 𝑐𝑚
given to the formula and then, cross
multiply it to make the equation
sin 20°(9𝑐𝑚) = 𝑜𝑝𝑝. Simplify and
come up with the answer 𝑜𝑝𝑝 =
5.79𝑐𝑚
Y=
3.07 cm
CHECKING:
Using Pythagorean theorem.
𝑐 = √𝑎 2 + 𝑏 2
𝑐 = √8.452 + 3.072
𝑐 = √71.40 + 9.42
𝑐 = 9 𝑐𝑚
Narrative interpretation:
To check the hypotenuse, use the
Pythagorean theorem formula
𝑐 = √𝑎2 + 𝑏 2 , substitute the given to the
formula. Simplify and come up with the
answer 𝑐 = 9 𝑐𝑚
Y= 7.37 cm
X= 5.16 cm
3. 𝟓𝟓°
Given: Angle = 55°
Length of cannon (Hypotenuse) = 9cm
Find: X & Y Components (sides of triangle)
Solution: Using Soh Cah Toa
X Component:
Y Component:
cos 55° =
𝑎𝑑𝑗
ℎ𝑦𝑝
sin 55° =
𝑜𝑝𝑝
ℎ𝑦𝑝
cos 55° =
𝑎𝑑𝑗
9𝑐𝑚
sin 55° =
𝑜𝑝𝑝
9𝑐𝑚
cos 55°(9𝑐𝑚) = 𝑎𝑑𝑗
𝑎𝑑𝑗 = 5.16 𝑐𝑚
sin 55°(9𝑐𝑚) = 𝑜𝑝𝑝
𝑜𝑝𝑝 = 7.37 𝑐𝑚
Narrative interpretation:
Narrative interpretation:
To find the x component, use the
To find the y component, use the
𝑜𝑝𝑝
formula sin 55° = ℎ𝑦𝑝, substitute the
𝑎𝑑𝑗
formula cos 55° = ℎ𝑦𝑝, substitute the
given to the formula and then, cross
multiply it to make the equation
cos 55°(9𝑐𝑚) = 𝑎𝑑𝑗. Simplify and come
up with the answer 𝑎𝑑𝑗 = 5.16 𝑐𝑚
given to the formula and then, cross
multiply it to make the equation
sin 55°(9𝑐𝑚) = 𝑜𝑝𝑝. Simplify and
come up with the answer 𝑜𝑝𝑝 =
7.37𝑐𝑚
CHECKING:
Using Pythagorean theorem.
𝑐 = √𝑎 2 + 𝑏 2
𝑐 = √5.162 + 7.372
𝑐 = √26.62 + 54.32
𝑐 = 8.99 𝑜𝑟 9 𝑐𝑚
Narrative interpretation:
To check the hypotenuse, use the
Pythagorean theorem formula
𝑐 = √𝑎2 + 𝑏 2 , substitute the given to the
formula. Simplify and come up with the
answer 𝑐 = 9 𝑐𝑚
Y= 8.46 cm
X=
3.08 cm
4. 𝟕𝟎°
Given: Angle = 70°
Length of cannon (Hypotenuse) = 9cm
Find: X & Y Components (sides of triangle)
Solution: Using Soh Cah Toa
X Component:
Y Component:
cos 70° =
𝑎𝑑𝑗
ℎ𝑦𝑝
sin 70° =
𝑜𝑝𝑝
ℎ𝑦𝑝
cos 70° =
𝑎𝑑𝑗
9𝑐𝑚
sin 70° =
𝑜𝑝𝑝
9𝑐𝑚
cos 70°(9𝑐𝑚) = 𝑎𝑑𝑗
sin 70°(9𝑐𝑚) = 𝑜𝑝𝑝
𝑎𝑑𝑗 = 3.08 𝑐𝑚
𝑜𝑝𝑝 = 8.46 𝑐𝑚
Narrative interpretation:
Narrative interpretation:
To find the x component, use the
To find the y component, use the
𝑜𝑝𝑝
formula sin 80° = ℎ𝑦𝑝, substitute the
𝑎𝑑𝑗
formula cos 80° = ℎ𝑦𝑝, substitute the
given to the formula and then, cross
multiply it to make the equation
cos 80°(9𝑐𝑚) = 𝑎𝑑𝑗. Simplify and come
up with the answer 𝑎𝑑𝑗 = 1.56 𝑐𝑚
given to the formula and then, cross
multiply it to make the equation
sin 80°(9𝑐𝑚) = 𝑜𝑝𝑝. Simplify and
come up with the answer 𝑜𝑝𝑝 =
8.86𝑐𝑚
CHECKING:
Using Pythagorean theorem.
𝑐 = √𝑎 2 + 𝑏 2
𝑐 = √3.082 + 8.462
𝑐 = √9.49 + 71.57
𝑐 = 9 𝑐𝑚
Narrative interpretation:
To check the hypotenuse, use the
Pythagorean theorem formula
𝑐 = √𝑎2 + 𝑏 2 , substitute the given to the
formula. Simplify and come up with the
answer 𝑐 = 9 𝑐𝑚
9 cm
5. 𝟗𝟎°
Given: Angle = 90°
Length of cannon (Hypotenuse) = 9cm
Find: X & Y Components (sides of triangle)
Solution: Using Soh Cah Toa
X Component:
Y Component:
cos 90° =
𝑎𝑑𝑗
ℎ𝑦𝑝
sin 90° =
𝑜𝑝𝑝
ℎ𝑦𝑝
cos 90° =
𝑎𝑑𝑗
9𝑐𝑚
sin 90° =
𝑜𝑝𝑝
9𝑐𝑚
cos 90°(9𝑐𝑚) = 𝑎𝑑𝑗
𝑎𝑑𝑗 = 0 𝑐𝑚
sin 90°(9𝑐𝑚) = 𝑜𝑝𝑝
𝑜𝑝𝑝 = 9 𝑐𝑚
Narrative interpretation:
Narrative interpretation:
To find the x component, use the
formula cos 90° = ℎ𝑦𝑝, substitute the
To find the y component, use the
𝑜𝑝𝑝
formula sin 90° = ℎ𝑦𝑝, substitute the
given to the formula and then, cross
multiply it to make the equation
cos 90°(9𝑐𝑚) = 𝑎𝑑𝑗. Simplify and come
up with the answer 𝑎𝑑𝑗 = 0 𝑐𝑚
given to the formula and then, cross
multiply it to make the equation
sin 90°(9𝑐𝑚) = 𝑜𝑝𝑝. Simplify and
come up with the answer 𝑜𝑝𝑝 = 9 𝑐𝑚
𝑎𝑑𝑗
CHECKING:
Using Pythagorean theorem.
𝑐 = √𝑎 2 + 𝑏 2
𝑐 = √02 + 92
𝑐 = √0 + 81
𝑐 = 9 𝑐𝑚
Narrative interpretation:
To check the hypotenuse, use the
Pythagorean theorem formula
𝑐 = √𝑎2 + 𝑏 2 , substitute the given to the
formula. Simplify and come up with the
answer 𝑐 = 9 𝑐𝑚
CONCLUSION AND RECOMMENDATION:
This miniature cannon is simple old pirate vibe. It is made of recyclable materials
combined to form a miniature cannon. The student recommends using recyclable
materials because it can find easily inside our home. The cannon can move on a
different angle to form a triangle and to launch it appropriately to the exact distance. It
does fire for 5 angles. The miniature cannon has a mechanism, not just like the real
cannon that needs gun powder to set fire.
In processing the design of miniature cannon, the student has affliction in figuring
what the right angle, measurements of the design and the recyclable materials that will
surely fit in the actual cannon. In the intervening period, the student conquers these
troubles and suppose a unique idea. The student suggests started making the cannon
early therefore, she can finish it neat and detailed without rushing.