kinematics 6of6 projectile motion final
Summary
TLDRThe script explains projectile motion, detailing how objects follow parabolic paths when launched at an angle or horizontally with constant acceleration due to gravity. It distinguishes between horizontal and angled projection, emphasizing the importance of separating horizontal and vertical motion for analysis. The script uses kinematics equations to describe constant velocity in the horizontal direction and constant acceleration in the vertical direction. It concludes with a story illustrating the concept, comparing projectile motion to falling objects.
Takeaways
- ๐ **Projectile Motion Definition**: An object moving under the influence of gravity alone, following a parabolic trajectory.
- ๐ **Types of Projectile Motion**: Horizontal projection (no initial angle) and angled projection (with an initial angle theta from the horizontal).
- ๐ **Parabolic Path**: The path of a projectile is parabolic due to constant acceleration from gravity acting vertically downwards.
- ๐ **Velocity and Acceleration**: In projectile motion, velocity direction changes (tangent to the path), but acceleration (due to gravity) remains constant and directed downwards.
- ๐ **Separation of Motion**: Horizontal and vertical motions are analyzed separately due to differing forces acting in each direction.
- ๐ **Horizontal Motion**: No horizontal acceleration (ignoring air resistance), so horizontal velocity remains constant.
- ๐ **Vertical Motion**: Constant acceleration due to gravity, with initial vertical velocity being zero for horizontal projection and non-zero for angled projection.
- โฑ๏ธ **Time Equivalence**: Time taken for horizontal and vertical motions are the same in projectile motion scenarios.
- ๐ **Monkey and Hunter Story**: An illustration of projectile motion, showing how the vertical motion of a falling object (monkey) and a projectile (arrow) are similar.
- ๐ฏ **Practical Application**: Understanding projectile motion is crucial for activities like archery, where aiming must account for the parabolic trajectory of the arrow.
Q & A
What is projectile motion?
-Projectile motion is the motion of an object projected into the air at an angle to the horizontal, which follows a parabolic trajectory under the influence of gravity alone.
What are the two types of projectile motion described in the script?
-The two types of projectile motion are: 1) projecting an object horizontally with a certain speed, and 2) projecting the object at an angle to the horizontal with a certain speed.
Why does the path of a projectile follow a parabolic curve?
-The path of a projectile follows a parabolic curve because the only acceleration acting on the object is due to gravity, which is constant and acts vertically downwards, while the horizontal component of the velocity keeps changing direction.
How do you determine the direction of velocity at a point in projectile motion?
-In projectile motion, the direction of velocity at any point is tangent to the curve of the path at that point.
Why is the acceleration due to gravity considered constant in projectile motion?
-The acceleration due to gravity is considered constant in projectile motion because it acts vertically downwards at a constant rate (denoted as 'g'), regardless of the object's horizontal motion.
Why is it necessary to separate horizontal and vertical motions when solving projectile motion problems?
-It is necessary to separate horizontal and vertical motions when solving projectile motion problems because the forces and accelerations acting in these directions are independent of each other.
What is the equation used to solve for horizontal motion in projectile motion?
-The equation used to solve for horizontal motion in projectile motion is distance equals speed times time (X = V*T), assuming negligible air resistance and constant velocity in the horizontal direction.
How is the vertical motion of a projectile different when the object is projected horizontally versus at an angle?
-When an object is projected horizontally, the initial vertical velocity is zero, and the motion is purely under the influence of gravity. When projected at an angle, the object has an initial vertical velocity component (V sin Theta), and the motion is a combination of this initial velocity and the acceleration due to gravity.
What is the significance of the story of the monkey and the hunter in the context of projectile motion?
-The story of the monkey and the hunter illustrates the concept of projectile motion by showing that both the arrow and the monkey falling are subject to the same vertical acceleration due to gravity, resulting in the arrow hitting the monkey despite its initial horizontal motion.
Why must an archer aim higher than the target to hit the bullseye?
-An archer must aim higher than the target to account for the vertical component of the arrow's projectile motion. This ensures that the arrow and the falling target meet at the correct point in space.
How does the time taken for the entire projectile motion relate to the time taken for the horizontal and vertical components?
-The time taken for the entire projectile motion is the same as the time taken for both the horizontal and vertical components of the motion, as the object moves through space in both directions simultaneously.
Outlines
๐ Understanding Projectile Motion
The paragraph explains the concept of projectile motion, which is the motion of an object thrown at an angle or horizontally where it follows a parabolic path due to constant acceleration by gravity. It describes two scenarios: one where an object is projected horizontally from a cliff, and another where it is projected at an angle from the ground. The key point is that the path is parabolic because the acceleration due to gravity is constant and acts vertically downwards, while the velocity changes direction as the object moves along the curve. The paragraph also introduces the idea of separating the motion into horizontal and vertical components, which is essential for solving problems involving projectile motion.
๐ Solving Projectile Motion
This paragraph delves into the mechanics of solving projectile motion problems. It emphasizes the importance of treating horizontal and vertical motions separately due to the absence of horizontal forces (assuming negligible air resistance) and the presence of constant vertical acceleration (gravity). The horizontal motion is described as constant velocity, allowing the use of the simple equation distance equals speed times time. In contrast, the vertical motion involves constant acceleration, enabling the use of various kinematic equations. The paragraph also discusses how to handle different initial conditions, such as zero initial vertical velocity for horizontal projections and non-zero initial vertical velocity for angled projections. The summary concludes with a note on the consistent time taken for both horizontal and vertical motions during projectile motion.
๐ The Monkey and the Hunter: A Projectile Motion Example
The final paragraph uses a story about a monkey and a hunter to illustrate the principles of projectile motion. The story describes a scenario where a monkey, hanging from a tree, plans to let go and fall to avoid an arrow shot by a hunter. However, the arrow, once released, will also undergo projectile motion and still hit the monkey. This narrative is used to explain that the vertical motion in projectile problems is analogous to objects falling or being thrown upwards and then falling back down. The paragraph suggests practical experiments, like aiming an arrow higher to compensate for the projectile motion or having a friend drop a target simultaneously with the arrow's release, to demonstrate the concept.
Mindmap
Keywords
๐กProjectile Motion
๐กParabolic Path
๐กAcceleration
๐กVelocity
๐กHorizontal Motion
๐กVertical Motion
๐กAir Resistance
๐กKinematics Equations
๐กGravity
๐กCliff
๐กAngle Theta
Highlights
Projectile motion is when an object follows a parabolic path due to constant acceleration in one direction (gravity).
There are two types of projectile motion: horizontal projection and angled projection from the horizontal.
In horizontal projectile motion, the object moves at a constant velocity horizontally.
In angled projectile motion, the object has both horizontal and vertical components of velocity.
The path of projectile motion is parabolic because the velocity direction changes while acceleration due to gravity remains constant.
The direction of velocity at any point in projectile motion is tangent to the curve.
The acceleration due to gravity is always vertically downward, regardless of the object's path.
Projectile motion occurs when an object is projected horizontally or at an angle with constant gravitational acceleration.
To solve projectile motion, separate the motion into horizontal and vertical components.
Horizontal motion in projectile motion is solved using constant velocity equations.
Vertical motion in projectile motion is solved using constant acceleration equations.
For horizontal motion, there are no horizontal forces acting on the object if air resistance is negligible.
The only force acting on the object during projectile motion is gravity, which acts vertically.
The time taken for the entire projectile motion is the same as the time taken for the horizontal and vertical components.
In angled projectile motion, the initial horizontal velocity component is V cos(Theta).
In angled projectile motion, the initial vertical velocity component is V sin(Theta).
The story of the monkey and the hunter illustrates the concept of projectile motion.
The vertical motion in projectile motion is similar to an object falling or being thrown upwards.
To hit a target with a projectile, one must account for the vertical motion by aiming higher than the target's current position.
Transcripts
now what is a projectile motion
projectile motion now is if you um
project an object at an angle or
horizontally but it takes the I mean the
the object takes a parabolic path so
that's called projectile motion example
right let's say this is a cliff and we
send or we or we actually project the
ball horizontally with speit v so what
will happen to the path of the ball the
ball will take a parabolic curve so this
is a projectile motion the second type
of projectile motion is when
you this is the ground and then you
project the ball at the angle Theta from
the horizontal with speed V so what will
happen to the path of the ball it will
also be a parabolic path so what will
happen is you will notice that this path
is also parabolic this is also parabolic
so this one is actually half of this all
right so this one is actually half of
this so when will you get a parabolic
path you get a parabolic path when the
acceleration is fix that One Direction
but your velocity keeps changing
direction example H when the ball is
traveling along this path the direction
of its velocity because velocity is a
vector right how do we get the direction
of the Velocity at this
point it is always tangent to the curve
do you
understand then when you reach this
point your velocity is also tangent to
the curve but your acceleration isn't it
due to gravity Al so you'll notice that
the acceleration of gravity is always
downwards or
not do you
agree so you will get a projectile
motion if um you send an object at um
either horizontal or angle but your
weight I mean which is your acceleration
is Only One Direction which is
vertically downwards any is constant so
you have a constant acceleration of G uh
vertically downwards all the time then
you get a projectile motion even in the
next case I mean the second case here
when you reach here your velocity is
also
tangent you reach here the velocity is
also tangent but what happens to the
acceleration acceleration is always G
and remember Accel gravity is always
vertically downwards so you will get
projectile motion do you understand that
so because uh an object which is is
undergoing projectile motion is actually
moving in a curve so when we want to
solve it we have to resolve the motion
that means we have to solve the
horizontal motion separately and then we
solve the vertical motion separately you
cannot solve them together but some
quantities they will be um will be
common for both which is the time taken
as it but when you solve horizontally
all your velocities your acceleration
everything must be horizontal when
you're solving vertically then all your
your velocity and acceleration must be
vertical you cannot mix them up together
for example let's look at the first case
here first which is this side when the
object is traveling through the air and
we want to solve horizontally so let's
take to the right as positive half so
we're going to solve horizontally taking
to the right as positive now are there
any forces acting horizontally on the
ball now the moment we give it an
initial speed we don't call it a force
because looking at the speed so we're
giving an initial speed as the ball is
flying through the air are there any
horizontal forces acting some people say
air resistance up so for the purpose of
calculation for our air levels we will
ignore air
resistance okay we will always assume
air resistance negligible so if your air
resistance negligible that means
there'll be no horizontal forces acting
right not because what is the only force
acting when the ball is traveling to the
air only the weight only the weight is
acting because whether your air resist
not weight is always acting so you only
got weight and weight is which direction
that's for horizontal got no Force so
because horizontal has no Force when you
solve horizontally you will be constant
velocity you understand that so and
remember I told you if the object is
traveling constant velocity can we use
kinematics equations no no what equation
can we use only one which is
distance equals to speed time time
that's all so your only equation will be
distance equals to
speed speed time time so let's call the
horizontal distance X will be equal to V
*
T okay now that's it no other equation
all right now now if you're solving
vertically then we can think about this
if you're solving
vertically now which direction should we
take as positive down downwards so if we
take downwards as
positive all right let take it downwards
is positive then it will be
constant
acceleration okay now and constant
acceleration means we can use any of the
kinematics equations so if I write V =
to U + a t so you will get v y Now what
is my initial vertical
speed zero zero because I'm projecting
horizontally that's why I'm trying to
say so it be zero plus GT why I use plus
h because I'm taking downwards as
positive and acceleration of gravity is
always downwards understand now you can
use any of the kinematics equation like
this but just remember that your initial
vertical speed is always
zero okay now for the second case here
let's do again now horizontally so once
again it will be
constant
constant constant velocity so if it is
constant velocity then what is the only
equation I can
use distance equals to speed time time
which will give me what
x equals to now there a there something
special because your speed is not hor
your initial speed is not horizontal it
is speed V at the angle Theta so we have
to resolve the speed into two components
V cos Theta and V sin Theta so what is
the horizontal component what is the
horizontal component of this
speed V cos Theta right not so your
equation will be V cos Theta * t you see
the difference between this and
this this one is just projecting
horizontally that's why you just we but
this one at the angle so it's V cos
Theta * understand but if you were to
solve
vertically so which direction should we
take as
positive up or down initial direction is
up or down up up so you must take up as
positive so we take upwards and
vertically remember we have constant
what acceleration so you can use any of
the kinematics equation example if you
use v = u + a so what is
my final vertical speed is v y so your
your initial vertical speed is how
much U is what V sin
Theta why because you are projecting the
object at the angle so initially does it
have a vertical component
which is V sin Theta so it's V sin Theta
and your acceleration must take negative
because your upwards is positive so it's
minus
GT another example let's say we use vยฒ =
u^2 + 2 a s so V y^ 2 equals to what
what is your initial vertical
speed V sin
Theta minus 2G y do you understand
it okay so the idea that I want you to
know is that whenever we solve
horizontally whether it is for this or
this it's always constant velocity so
there's only one equation but when you
solve vertically for this or this you'll
be constant acceleration but there's a
difference you're soling for this type
your initial vertical speed is always
zero but solving for this type you will
have an initial vertical
speed understand all right so that's how
you solve projectile motion now the time
taken for you to move right let's say
from here to here so you can split it
that means it will be the same as the
time taken to travel horizontally from
here to here which is the same as the
time taken to travel vertically from
here to here that one is the same okay
now a very good illustration now of this
projectile motion all right I'll show
you the next slide now the next
illustration I'm going to show you help
you to imagine the pro proor motion now
have you heard of the story of the
monkey and the
hunter never so the the story of the
monkey and the hunter goes like this l
so let's say you have this uh tree here
and there's this Branch here and the
monkey is hanging from the
branch okay this is supposed to be a
monkey okay something like this huh it's
not okay it is so now let's say you have
a
hunter standing uh standing here wait
let me I show you something a bit easier
so let's say standing here all right oh
sorry the hand
wrong so he's holding a bow and an arrow
and aiming where and actually it is
aiming right at the head of the monkey
very want learn okay but so what the
monkey thinks it's like this he thinks
that the moment the hunter releases the
arrows since the arrow is pointing at
his head he will release his hand the
grip from the TR so he'll release his
grip here and he will fall and because
he falls the arrow will pass over his
head that's what he
thinks okay so what do you think
happened so as he fell the this Arrow
will undergo projectile motion as well
so that means when
the monkey
fell suddenly become bigger okay
the arrow undergo a projectile motion
and will hit his head
exactly you understand so why am i
showing you this is because the vertical
motion of a projectile motion here is
similar to um object falling or going up
and coming down it's the same do you
understand this is exactly the same so
some people find this hard to imagine so
I tell them if you use a nonviolent one
you can go to the uh what do you call it
the archery there and let's say you're
aiming at the B side okay so you aim the
arrow exactly at the bull side now do
you think you will hit the bull side if
you release definitely no why because
you undergo projector motion and you
will
fall so if you want to hit the bullseye
you must actually aim slightly
higher because after projector motion
then you will hit the target up or
there's an alternative you ask your
friend to hold
it hold the Target now the moment you
release the arrow you ask your friend to
drop the
target so as your arrow moves in a
projectile motion and your Target Falls
it will hit exactly The Bu eye you can
give it a try
afterwards okay why because the vertical
motion of this Arrow which is from here
to here so the vertical motion is
actually just Arrow falling it's the
same as your target flow falling that
that's why I'm trying to show you so
that's why when you solve projectile
motion you just solve as if uh for the
vertical motion you just solve as if you
either dropping the ball if you're
projecting horizontally so the vertical
motion is just falling if you're
projecting at the angle then how you
will solve vertical motion is as if you
throw a ball up into the end falling
back it's the same one no difference
okay
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