Two Dimensional Motion (1 of 4) An Explanation
Summary
TLDRThis video offers a qualitative exploration of two-dimensional projectile motion, explaining how objects follow a parabolic path when launched at an angle with an initial velocity. It delves into the independent motions in the x and y directions, emphasizing the role of gravity as the only unbalanced force affecting the object's trajectory. The script clarifies that while there is no acceleration in the x-direction due to balanced forces, the y-direction experiences constant acceleration due to gravity, leading to changes in the object's velocity. The video aims to demystify the physics behind projectile motion, providing a fundamental understanding of the forces and motions involved.
Takeaways
- 🚀 The video discusses two-dimensional projectile motion, where an object is launched at an angle above the horizon with an initial velocity, following a parabolic path.
- 🔍 The parabolic path is due to the object's simultaneous motion in the X and Y directions, which are independent of each other.
- 🧲 The only force acting on the object during its flight is gravity, which acts vertically downward, causing changes in the object's motion.
- 🔄 In the X direction, there are no forces acting on the object once it is in the air, resulting in a constant velocity due to balanced forces.
- 🌟 The initial velocity in the X direction can be calculated and remains constant throughout the object's trajectory.
- 📉 In the Y direction, the unbalanced force of gravity causes the object to accelerate downwards, resulting in a changing velocity.
- 🌐 The object's motion in the Y direction is akin to free fall, with a constant acceleration equal to the acceleration due to gravity (approximately -9.81 m/s²).
- 📊 The video script includes a table illustrating the constant velocity in the X direction and the changing velocity in the Y direction over time.
- ⏱ The initial velocity in the Y direction is given as an example, showing how the velocity changes over time due to acceleration.
- 🔢 The script explains that the velocity in the Y direction decreases as the object ascends and increases as it descends, reaching zero at the peak of its trajectory.
- 👍 The video concludes by encouraging viewers to subscribe, like, and comment if they found the explanation helpful.
Q & A
What is the main focus of the video script?
-The video script focuses on providing a qualitative description of two-dimensional projectile motion, explaining why an object follows a parabolic path when projected at an angle above the horizon.
Why does the object follow a parabolic path?
-The object follows a parabolic path because it is moving simultaneously in the X and Y directions, with each motion being independent of the other and influenced by different forces.
What are the two independent motions happening in two-dimensional projectile motion?
-The two independent motions are the horizontal motion in the X direction and the vertical motion in the Y direction.
What is the primary force acting on the object during its projectile motion?
-The primary force acting on the object during its projectile motion is gravity, which acts in the negative Y direction.
Why is there no force acting in the X direction after the object is projected?
-After the object is projected, there is no force acting in the X direction because objects in motion tend to stay in motion in a straight line unless acted upon by an unbalanced force, and in the air, only gravity acts on the object.
What is the effect of balanced forces on the object's acceleration in the X direction?
-When forces are balanced, the acceleration in the X direction is zero, resulting in a constant velocity with no change in speed.
How does the acceleration due to gravity affect the object's motion in the Y direction?
-The acceleration due to gravity causes the object to experience free fall in the Y direction, with an acceleration of -9.81 m/s², leading to a change in velocity as it moves up and then down.
What is the initial velocity in the X direction called, and how is it determined?
-The initial velocity in the X direction is called the initial X velocity (V_ix), and it can be determined from the initial total velocity and the projection angle.
How does the object's velocity change as it moves up in the Y direction?
-As the object moves up in the Y direction, its velocity decreases due to the acceleration caused by gravity, until it reaches the top of its path where the velocity in the Y direction is zero.
What happens to the object's velocity as it comes back down in the Y direction?
-As the object comes back down in the Y direction, its velocity increases in the negative direction due to the acceleration caused by gravity, speeding up as it falls.
What is the significance of the table provided in the script?
-The table in the script provides a timeline of the object's motion, showing how the velocity in the X and Y directions changes over time, given the initial velocities and accelerations.
Outlines
🚀 Introduction to 2D Projectile Motion
The video begins by introducing the concept of two-dimensional projectile motion, where an object is launched at an angle with an initial velocity. The object follows a parabolic path due to two independent motions in the horizontal (x) and vertical (y) directions. The video emphasizes that while there is no force acting in the x-direction (resulting in constant velocity), gravity acts in the y-direction, causing a constant acceleration downwards. The importance of forces and their role in changing motion is highlighted, with gravity being the only unbalanced force acting on the object during its flight.
📉 Understanding Motion in X and Y Directions
This paragraph delves deeper into the motion in the x and y directions. It explains that in the x-direction, the object maintains a constant velocity because there are no unbalanced forces acting on it, once it is in motion. The initial velocity in the x-direction is given as an example, and it is stated that this velocity remains unchanged throughout the object's trajectory. In contrast, the y-direction experiences unbalanced forces due to gravity, resulting in an acceleration of 9.81 m/s² downwards. The object's velocity in the y-direction changes over time, slowing down as it ascends and speeding up as it descends, following the principles of free fall. The paragraph concludes with a table illustrating the constant velocity in the x-direction and the changing velocity in the y-direction over a period of time.
Mindmap
Keywords
💡Projectile Motion
💡Initial Velocity
💡Parabolic Path
💡Forces
💡Unbalanced Forces
💡Balanced Forces
💡Acceleration
💡Free Fall
💡Velocity Components
💡Constant Velocity
💡Symmetry
Highlights
The video provides a qualitative description of two-dimensional projectile motion.
An object is projected with an initial velocity at an angle above the horizon, following a parabolic path.
The parabolic path is due to the object moving simultaneously in the X and Y directions, with independent motions.
Forces cause changes in motion; unbalanced forces result in changes in velocity.
The only force acting on the object during its flight is gravity, acting in the negative Y direction.
There is no force acting in the X direction once the object is in motion, leading to a constant velocity.
The initial velocity can be broken down into components in the X and Y directions.
In the X direction, the velocity remains constant due to balanced forces and zero acceleration.
The Y direction experiences unbalanced forces, resulting in acceleration due to gravity.
The object undergoes free fall in the Y direction, with a constant acceleration of -9.81 m/s².
The velocity in the Y direction changes due to acceleration, unlike the constant velocity in the X direction.
The object's velocity in the Y direction decreases as it ascends and increases as it descends.
The motion is symmetrical, with the object reaching zero velocity at the peak of its trajectory.
The velocity vectors in the Y direction illustrate the object's deceleration and acceleration.
A table is presented to show the relationship between time, velocity, and acceleration in both directions.
The video concludes with a summary of the key points about two-dimensional projectile motion.
The presenter encourages viewers to subscribe, like, and comment for more educational content.
Transcripts
okay in today's video I'm going to go
over a qualitative description of
two-dimensional projectile motion when
an object is projected with some initial
velocity at some angle above the Horizon
and this is the situation that we have
we have this object it's going to be
projected with some initial velocity at
some angle above the Horizon and when it
does that it leaves the ground and it
follows this nice parabolic path and we
want to talk about why does it follow
that nice parabolic path and it really
does that because it's doing two things
this object is doing two things at the
same time and those two things that it's
doing are really independent of each
other and the two things that it's doing
is it's moving in the X Direction and in
the y direction at the same time but
like I said those two motions are
independent of each other and we're
going to go through the differences
between the motion in the X and the
motion in the y direction now before we
do that we really have to talk a little
bit about the forces because it's the
forces that cause the change in motion
obviously this object is not moving in
the straight line so it's motion its
velocity is
changing and what causes those change
well changes in motion changes in
velocity are caused by unbalanced forces
and as this object travels through the
air there's only one force acting on the
object at each point in time and that is
the force of gravity the force of
gravity acts negative Y no negative y
direction now a lot of people think well
there must be some force acting in the X
Direction because the ball is actually
obviously moving across horizontally in
the X Direction but once it leaves this
point where it's been projected there
are no other forces that cause the
object to move in the X Direction
objects in motion stay in motion objects
stay and rest unless acted upon by an
unbalanced force so a lot of people
think well when the ball up here there
must be some force acting in the X
Direction because the ball is moving
also horizontally in the X Direction
there is no other forces there's only
one force acting on the object and that
is the force of gravity and that is
acting in the y direction negative y
down okay now that means for the X
Direction there are no forces acting on
the ball sure there was some Force down
here that got it started but once it
leaves the ground there's no forces
acting in the X Direction so that means
the forces are balanced the sum of the
forces if there are no forces the sum of
the forces is zero they're balanced
forces if the forces are balanced then
the acceleration is zero in the X
Direction the object is not
accelerating that means it has a
constant
velocity now if we can figure out which
we'll do in the next video we'll talk
about we know the initial velocity we
can determine the component of the
initial velocity that is acting in the X
direction we might call that V iix
velocity initial
X what's the velocity at every other
point in time during the object's
path well the forces are balanced the
acceleration is zero the velocity is
constant that means VI is equal to all
the other velocities so if we know the
initial velocity in the X Direction then
we know the Velocity in the X Direction
at every other point in
time so I drew these vectors VX with the
same length the same magnitude because
the Velocity in the X Direction doesn't
change now what about in the y direction
well somewhat obviously there's only one
force acting on the object in the y
direction so the forces cannot be
balanced that means they're unbalanced
and if they're unbalanced the object is
accelerating now in this case
two-dimensional projectile motion
projectile motion in the y direction the
object is really experiencing freef fall
and the acceleration is equal to the
acceleration due to gravity during freef
fall that's what we mean by freef Fall
the object is falling freely out of the
sky so to speak so the acceleration in
the y direction which we sometimes use G
the acceleration due to gravity but I
have acceleration the y direction is
equal to minus 9.81 m/s squared because
the acceleration is in the negative
Direction okay we'll talk more about
that in the next slide but it's a
constant acceleration but it is
accelerating and therefore the object is
changing in its velocity now I'm going
to get rid of these Force vectors I'm
going to draw in the velocity vectors
there is some initial velocity in the y
direction well as the object goes up in
the y direction it slows down so I'm
going to draw the next velocity Vector a
little smaller the next one a little
smaller and when it reaches the top of
its path it has no velocity in the y
direction it has a velocity in the X
Direction but the Velocity in the y
direction at the top of its path is zero
and then the velocity starts to increase
in the negative Direction these are all
positive this is negative and then it
comes down and it's speeding up it's
accelerating in the negative
Direction okay here it's also
accelerating in the negative Direction
but slows down stops and then it speeds
back up as it comes back down like that
okay so that's the important things you
should know about the Velocity in the X
excuse me the motion in the X and the
motion in the Y balance forces no
acceleration unbalanced forces
acceleration now let's also look at this
table really quickly here's the
information we had from the previous
slide here's the time zero and then 1 2
3 4 five six seconds 1 2 3 4 5 6 seconds
that's the time over here now I'm
telling you that the initial velocity in
the X direction is 25 M per second I'm
just giving you that that would be
something you might get on the
problem now the acceleration is zero
because the forces are
balanced so what does that mean the
velocity is constant so if the initial
velocity is 25 m/ second and we're
saying the acceleration is zero so now I
can write down here zero the
acceleration is zero in each case well
the acceleration is zero that means the
velocity is not changing that means at
each point in time in the X Direction
the object is moving 25
[Music]
m/s now what about in the y direction
and we said for free fre fall for
projectile motion it's basically
experiencing freef fall that means the
acceleration at each point in time is-
9.81 m/s
squar well I'm going to tell you again
that the initial
velocity in the y
direction is 29.4 3
m/s now the object is accelerating in
the negative Direction 9.81 m/s squared
that means when it goes up as it's
traveling up the object is slowing down
9.81 m/s for every second so 1 second
later it's traveling
9.81 m/s
slower after 2 seconds it's traveling
another 9.81 m/ second
slower and when it reaches the top in
the y direction the velocity is
zero well now it's going to start back
down and it's going to speed
up okay and now it's going to speed up
in the negative Direction so the
velocities are going to be negative so
if it starts at zero right here and it
comes back down one second later because
it's accelerating 9.81 meters per second
squared it's going 9.81 m/ second in the
negative Direction after 2 seconds it's
two times this and after 3 seconds it's
three times that you'll notice it's
symmetrical if it leaves the ground at
29 it comes back and reaches the ground
at 29 the positive sign means it's going
in the positive direction which is up
the negative sign simply means that it's
going in a negative Direction which is
down this positive sign does not mean
speeding up and slowing down the sign of
the Velocity is equal to the direction
of the motion okay so there you have it
X Direction zero
acceleration constant
velocity why High Direction it is
accelerating therefore the velocity is
changing okay so there you go that is a
nice quick qualitative explanation of
two-dimensional projectile motion I hope
you found it helpful thank you very much
for watching if you did find it helpful
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