Projectile Motion Part II | Quarter 4 Grade 9 Science Week 2 Lesson
Summary
TLDRThis video from the Maestro Techie YouTube channel dives into the intricacies of projectile motion, specifically focusing on the effects of the angle of launch on a projectile's range and height. The lesson begins with a review of the basic concepts of projectile motion, such as trajectory and the distinction between horizontal and vertical components. The video explains that while the horizontal velocity remains constant, the vertical velocity changes due to gravity's influence. It then explores the variables involved in launching a projectile at an angle and presents equations to solve problems related to projectile motion. The video highlights that the maximum range is achieved at a 45-degree angle and that a projectile launched at 30 degrees will have the same range as one launched at 60 degrees, due to these angles being complementary. An example problem is solved, calculating the maximum height and horizontal displacement of a baseball hit at a 25-degree angle with an initial velocity of 30 meters per second. The video concludes with a reminder of the impact of the angle of release on a projectile's trajectory, emphasizing the educational value of understanding these principles.
Takeaways
- 📚 Start with a review: If you missed the first week's lesson on projectile motion, check out the link in the description for an introduction to concepts like trajectory and the definition of projectile motion.
- 🚀 Understand the basics: A body in projectile motion follows a parabolic path with horizontal and vertical components, where the horizontal velocity is constant (acceleration equals zero) and the vertical acceleration is constant due to gravity (9.8 m/s²).
- 🔍 Analyze the game: Baseball is an example of projectile motion launched at an angle, illustrating how vertical velocity changes due to gravity's influence.
- 📈 Grasp the variables: In projectile launch at an angle, consider both the horizontal and vertical components of the motion.
- 📐 Initial conditions: An object projected from rest at an upward angle has an initial velocity that can be resolved into horizontal and vertical components.
- ⏱️ Time and velocity: The time it takes for an object to stop at its highest point is the same as the time it takes to return to the launch point, with the initial upward velocity being equal to the final velocity when it returns to its original height.
- 📐 Equations for solving: Learn and apply the equations for projectile motion to solve problems involving range, maximum height, and horizontal displacement.
- 🎯 Optimal angle for range: The greatest range is achieved when the projectile is launched at a 45-degree angle to the horizontal.
- 📏 Complementary angles: Angles of 30 and 60 degrees are complementary and result in the same range, as do 15 and 75 degrees.
- 📈 Vertical displacement: As the angle of launch increases, the vertical displacement of the projectile also increases.
- ⏰ Time to reach max height: The time to reach the maximum height is half of the total time of flight.
- 📝 Example problem: For a baseball hit at an angle of 25 degrees with a velocity of 30 m/s, use the given formulas to calculate the maximum height and horizontal displacement of the ball.
Q & A
What is the general trajectory of a projectile in motion?
-A projectile in motion follows a parabolic trajectory, which is the result of the combination of its horizontal and vertical components of motion.
What is the acceleration of the horizontal component of projectile motion?
-The acceleration of the horizontal component of projectile motion is zero, as there are no forces acting in the horizontal direction once the projectile is launched.
What is the acceleration due to gravity and what is its value in meters per second squared?
-The acceleration due to gravity is the constant acceleration that acts on the vertical component of projectile motion, and its value is 9.8 meters per second squared.
In the context of projectile motion, what is the term for the initial speed of the object when it is launched?
-The initial speed of the object when it is launched is referred to as the initial velocity, which can be resolved into horizontal and vertical components.
What is the relationship between the angle of launch and the time it takes for a projectile to reach its highest point?
-The time it takes for a projectile to reach its highest point is the same amount of time it takes to return to the point from which it was launched, regardless of the angle of launch.
What is the maximum range achieved by a projectile launched at an angle?
-The maximum range of a projectile is achieved when it is launched at an angle of 45 degrees with respect to the horizontal.
What are complementary angles in the context of projectile motion, and how do they relate to range?
-Complementary angles in projectile motion are two angles that add up to 90 degrees, such as 30 and 60 degrees. A projectile launched at one of these angles will have the same range as if it were launched at the other angle.
What is the formula used to calculate the maximum height reached by a projectile?
-The formula to calculate the maximum height (h) reached by a projectile is h = (v_i * sin(θ))^2 / (2 * g), where v_i is the initial velocity, θ is the angle of launch, and g is the acceleration due to gravity.
How is the horizontal displacement or range of a projectile calculated?
-The horizontal displacement or range (R) of a projectile is calculated using the formula R = v_i * cos(θ) * t, where v_i is the initial velocity, θ is the angle of launch, and t is the total time of flight.
What happens to the vertical velocity of a projectile at its highest point?
-At the highest point of its trajectory, the vertical velocity of a projectile is momentarily zero because it momentarily stops before starting to fall back down due to gravity.
What is the significance of the angle of launch in determining the range and height of a projectile?
-The angle of launch significantly affects both the range and height of a projectile. A higher angle increases the vertical displacement, while a 45-degree angle maximizes the range. Complementary angles result in the same range due to symmetry in the projectile's trajectory.
How does the direction of gravity influence the vertical velocity of a projectile?
-The direction of gravity, which is downward, opposes the upward motion of a projectile, causing the vertical velocity to decrease as the projectile rises. Conversely, as the projectile falls back to the ground, the direction of gravity aids its motion, increasing the vertical velocity.
Outlines
📚 Introduction to Projectile Motion at an Angle
This paragraph introduces the topic of projectile motion launched at an angle, which is the focus of the Grade 9 science quarter for week 2. It sets the learning objective to investigate the relationship between the angle of release and the projectile's height and range. The paragraph also recaps the basic concepts of projectile motion, such as trajectory and the parabolic path created by the combination of horizontal motion with constant velocity and vertical motion with constant acceleration due to gravity. The example of a baseball game is used to illustrate these concepts, highlighting how the vertical velocity of the projectile changes due to gravity's influence.
🔍 Variables and Equations for Projectile Launch
This section delves into the variables involved in launching a projectile at an angle, emphasizing the distinction between the horizontal and vertical components of motion. It explains that an object projected from rest at an upward angle will have an initial velocity that can be resolved into horizontal and vertical components. The horizontal velocity remains constant, while the vertical velocity changes due to gravity. The paragraph also discusses the time it takes for the object to stop at its highest point and return to the launch point, and how the initial and final vertical velocities are of the same magnitude. Several equations are introduced to solve problems related to projectile motion at an angle, including those for maximum height and horizontal displacement (range).
🏞️ Angles for Maximum Range and Height
This paragraph explores the optimal angles for achieving maximum range and height in projectile motion. It reveals that a 45-degree angle results in the greatest range, while a 75-degree angle leads to the maximum height. The concept of complementary angles (30 and 60 degrees) is introduced, showing that they yield the same range. The paragraph also explains how the angle of launch affects the projectile's vertical displacement and the time it takes to reach the maximum height. An example problem is presented, where a baseball player hits a home run, and the video demonstrates how to calculate the maximum height reached by the ball and the horizontal displacement using the given launch angle and velocity.
🎓 Conclusion and Acknowledgment
The final paragraph wraps up the lesson on projectile motion, summarizing the key takeaway that the angle of release impacts both the range and height of a projectile. It reiterates the significance of a 45-degree angle for maximum range and provides a brief overview of the calculations performed in the example problem. The video concludes with a call to action for viewers to like, share, and subscribe for updates on future lessons. It also includes a shout out to specific individuals and groups, acknowledging their contribution to the video's success.
Mindmap
Keywords
💡Projectile Motion
💡Trajectory
💡Horizontal and Vertical Components
💡Acceleration Due to Gravity
💡Angle of Release
💡Range
💡Maximum Height
💡Complementary Angles
💡Initial Velocity
💡Time of Flight
💡Baseball
Highlights
Investigate the relationship between the angle of release and the height and range of the projectile.
Projectile motion has a parabolic trajectory with horizontal and vertical components.
Horizontal component of projectile motion has zero acceleration, while vertical component has constant acceleration due to gravity (9.8 m/s²).
Baseball is an example of projectile motion launched at an angle.
Vertical velocity of a projectile decreases as it rises due to gravity, is zero at the maximum height, and increases as it falls back down.
Initial velocity of a projectile launched at an angle can be resolved into horizontal and vertical components.
Horizontal velocity is constant, while the vertical velocity changes due to gravity.
Time taken to reach the highest point is the same as the time taken to return to the launch point.
The initial upward velocity is the same magnitude as the final velocity when the projectile returns to its original height.
The angle that results in the greatest range is 45 degrees.
The angle that results in the maximum height is 75 degrees.
Projectiles launched at 30 and 60 degrees have the same range due to being complementary angles.
As the angle of launch increases, the vertical displacement of the projectile also increases.
At the highest point, the vertical component of velocity is zero, and the time to reach it is half the total flight time.
Example problem: Calculating the maximum height and horizontal displacement of a baseball hit at an angle of 25 degrees with a velocity of 30 m/s.
Formula for maximum height: VI * sin(Theta)^2 / (2 * g).
Formula for horizontal displacement (range): VI * cos(Theta) * time.
Total time of flight can be calculated using VI * sin(Theta) / g.
The final calculated maximum height reached by the baseball is 8.20 meters, and the horizontal displacement is 70.42 meters.
Transcripts
good day students welcome back to
Maestro techie YouTube channel let us
continue our discussion if you haven't
watched our week 1 video Lesson about
the horizontal and vertical motions of a
projectile check out the link in the
description box below we are now going
to have Grade 9 science quarter for week
2 lesson which is all about projectile
motion launched at an angle here's our
learning objective investigate the
relationship between the angle of
release and the height and range of the
projectile so get ready to learn this
lesson and keep on watching
[Music]
from the previous lesson you are
introduced to the basic concepts of
projectile motion such as trajectory and
and the definition of projectile motion
itself a body in projectile motion has
been established to have a parabolic
trajectory with a horizontal and
vertical components the horizontal
component of a projectile motion has the
acceleration equal to zero since the
velocity is constant on the other hand
the vertical component of acceleration
is constant which is acceleration due to
gravity and that is always equal to 9.8
meter per second squared therefore
projectile motion is the combination of
horizontal motion with constant velocity
and vertical motion with constant
acceleration take a look at this are you
familiar with this game
yes baseball this is an example of
projectile motion launched at an angle
for angle launch projectile horizontal
velocity or VX is still constant while
the vertical velocity can be described
in three parts first from the picture as
you observed
the projectile rises from point A to
point B the vertical velocity or v y is
decreasing this is because the direction
of gravity is opposite to the projectile
motion next as the projectile reaches
the maximum height which is the point B
it momentarily stops causing a vertical
velocity or v y equal to zero and third
when it returns back to the ground from
point B to point C it agrees to the
direction of gravitational force hence
Vertical Velocity is increasing
so when the vertical velocity of the
baseball as it rises to the air
decreases due to the opposing direction
of gravity towards the motion when the
baseball reaches the maximum height it
momentarily stops causing the vertical
velocity to be zero when it reaches to
the ground its vertical velocity
increases since the direction of the
baseball's motion is the same with
gravity take note of that class
now take a look at the variables
involved in projectile launch at an
angle
we have here the horizontal component
and the vertical component
[Music]
next we have the facts about projectile
launched at an angle first up an object
is projected from rest at an upward
angle Theta just like this scenario the
ball started from rest where stiff and
carry is holding the ball
second
its initial velocity can be resolved
into two components as you can see we
have the horizontal and the vertical
component third the horizontal velocity
is constant due to gravity a constant
horizontal velocity that moves in the
same direction as the launch the
acceleration of which is zero fourth the
amount of time the object takes to come
to a stop at its highest point is the
same amount of time it takes to return
to where it was launched from
and lastly the initial velocity upward
will be the same magnitude as the final
velocity when it returns to its original
height so these are the facts about
projectile launched at an angle next
here are some of the equations that may
help you solve problems involving
projectile launched at an angle
let's proceed
take a look at this photo class what can
you say
which angle results in the greatest
range
when we say range it is the horizontal
displacement and as you can see the
farthest range is in the 45 degrees
angle next question
which angle results in the maximum
height
hmm
as you can see it is the 75 degrees
angle
how would you compare the distance
traveled by projectile launched at 30
and 60 degrees as you can see they have
the same range same as 15 and 75 they
have the same range
this scenario that I have shown you is
also an example of projectile motion
launch at an angle and these are the
possible results if you launch an object
at different angle take note class angle
that is usually represented by Theta is
a numerical value in degrees expressing
the orientation of a projectile to be
from to sum it up class the angle of
release affects the range and height of
a projectile the maximum range is
achieved if the projectile is fired at
an angle of 45 degrees with respect to
the horizontal component an object
launched at an angle of 30 degrees will
also be the same if it is launched at 60
degrees
the angles 30 and 60 degrees are called
complementary angles because they add up
to 90 degrees
as the angle of launch increases the
vertical displacement of the projectile
will also increase at the highest point
the vertical component of velocity is
zero and the time to reach the maximum
height is half of the total time of
flight now let us have an example
problem
a baseball player leads off the game and
hits a long home run the ball leaves the
bat at an angle of 25 degrees with a
velocity of 30 meter per second let us
find the maximum height reached by the
ball and the horizontal displacement of
the boat let us illustrate the problem
as you can see we have an angle of 25
degree and a velocity of 30 meter per
second we are looking for the maximum
height reached by the ball and the
horizontal displacement or range or DX
of the ball let us try to solve this
problem here are the given our initial
velocity or VI which is equal to 30
meter per second our degree of angle
which is 25 degrees acceleration due to
gravity which is 9.8 meter per second
squared the formula that we are going to
use is VI times sine Theta squared
divided by twice the acceleration due to
gravity now let's substitute the given
to our formula d y is equal to our VI
which is 30 meter per second and sine
Theta which is sine 25 degrees do not
forget to square it to itself divided by
2 times 9.8 meter per second squared
multiplying these two quantities and
squaring it we have the product of
160.745 and so on meter squared per
second squared divided by the product of
2 and 9.8 and that is 19.6 meter per
second squared let us divide this two
the quotient
8.20 and as you can see we have to
simplify the units let's cancel out
and the remaining unit is meter
therefore our final answer or the
maximum height reached by the ball is
8.20 meters
now let us solve the second one
what is the horizontal displacement or
range of the bolt again here are our
given the formula that we are going to
use to find the DX is just multiplying v
i cosine Theta and the time as you can
see we do not have the value of time
therefore we have to solve the total
time to proceed in VX and this is the
formula that we are going to use so let
us solve it total time is equal to 2
times our VI and sine Theta all over the
acceleration due to gravity 30 times
sine 25 degrees is equal to
12.678 meter per second divided by of
course our acceleration due to gravity
12.678 divided by 9.8 times 2 we have
2.59 let us not forget to simplify our
unit by canceling
and our unit is seconds therefore the
total time traveled by the ball is 2.59
seconds now we can now solve for the
value of DX DX is equal to our VI cosine
Theta and the value of time multiplying
these three quantities our final answer
is
70.42 let us not forget to cancel the
units therefore our final answer is
70.42 meters and that ends our lesson
about projectile motion I hope you
learned something new today please give
this video a thumbs up share this to
your classmates and do not forget to
subscribe to keep you updated for our
next video Lesson comment down for a
shout out
shout out to Gabrielle balitas
Al-Qaeda Nifty red gien and mamirna
bigtas and all the grade 9 students of
San bartolome high school and also shout
out to all the science teachers of the
Vitae National High School thank you all
so much for watching see you on my next
video bye
[Music]
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