Two Dimensional Motion (1 of 4) An Explanation

Summary

This 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

00:00

🚀 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.

05:01

📉 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.

Keywords

💡Projectile Motion

Projectile motion refers to the motion of an object projected into the air and is influenced only by the acceleration due to gravity. In the video, this concept is central as it explains why an object follows a parabolic path when launched at an angle above the horizon.

💡Initial Velocity

Initial velocity is the speed with which an object is launched and its direction. In the context of the video, the initial velocity is decomposed into horizontal (X-direction) and vertical (Y-direction) components, which are crucial for understanding the object's trajectory.

💡Parabolic Path

A parabolic path is the trajectory followed by an object in projectile motion under the influence of gravity. The video script describes this path as 'nice' and explains that it results from the combination of horizontal motion at constant velocity and vertical motion with constant acceleration due to gravity.

💡Forces

Forces are pushes or pulls that can change the motion of an object. In the script, it is emphasized that the only force acting on the projectile is gravity, which causes the change in motion in the Y-direction, while no force acts in the X-direction after the object is launched.

💡Unbalanced Forces

Unbalanced forces are forces that are not counteracted by an equal and opposite force, resulting in a change in motion. The video explains that in the Y-direction, gravity is an unbalanced force causing the object to accelerate downwards.

💡Balanced Forces

Balanced forces occur when all forces acting on an object are equal in magnitude and opposite in direction, resulting in no acceleration. The script mentions that in the X-direction, the forces are balanced, leading to a constant velocity.

💡Acceleration

Acceleration is the rate of change of velocity of an object. The video script differentiates between the X and Y directions, noting that there is no acceleration in the X-direction (constant velocity) and a constant acceleration in the Y-direction due to gravity.

💡Free Fall

Free fall is the motion of an object falling solely under the influence of gravity, without any other forces acting on it. In the video, the Y-direction motion of the projectile is described as free fall, where the object experiences a constant acceleration downwards.

💡Velocity Components

Velocity components are the separate horizontal and vertical velocities of an object in motion. The script breaks down the initial velocity into its X and Y components, 'V_ix' and 'V_iy', which are essential for analyzing the projectile's path.

💡Constant Velocity

Constant velocity means that an object moves at a steady speed in a straight line. The video explains that in the X-direction, the object has a constant velocity because the forces are balanced and there is no acceleration.

💡Symmetry

Symmetry in motion refers to the mirror-like behavior of an object's velocity as it moves upwards and then downwards in projectile motion. The script illustrates this by showing that the object's velocity in the Y-direction decreases as it ascends and then increases symmetrically as it descends.

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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