kinematics 6of6 projectile motion final

Summary

The 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

• 🚀 **Projectile Motion Definition**: An object moving under the influence of gravity alone, following a parabolic trajectory.
• 📏 **Types of Projectile Motion**: Horizontal projection (no initial angle) and angled projection (with an initial angle theta from the horizontal).
• 📉 **Parabolic Path**: The path of a projectile is parabolic due to constant acceleration from gravity acting vertically downwards.
• 🔍 **Velocity and Acceleration**: In projectile motion, velocity direction changes (tangent to the path), but acceleration (due to gravity) remains constant and directed downwards.
• 🔄 **Separation of Motion**: Horizontal and vertical motions are analyzed separately due to differing forces acting in each direction.
• 🌐 **Horizontal Motion**: No horizontal acceleration (ignoring air resistance), so horizontal velocity remains constant.
• 📉 **Vertical Motion**: Constant acceleration due to gravity, with initial vertical velocity being zero for horizontal projection and non-zero for angled projection.
• ⏱️ **Time Equivalence**: Time taken for horizontal and vertical motions are the same in projectile motion scenarios.
• 🐒 **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.
• 🎯 **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

00:00

🚀 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.

05:01

📐 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.

10:04

🐒 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.

Keywords

💡Projectile Motion

Projectile motion is a type of motion experienced by an object that is projected or thrown near the Earth's surface and moves along a curved path under the action of gravity only. In the video, the concept is introduced with examples such as throwing a ball horizontally from a cliff or at an angle to the ground. The motion is parabolic, and it is explained that the path is due to constant acceleration due to gravity acting vertically downwards.

💡Parabolic Path

A parabolic path is the trajectory followed by an object in projectile motion. The video describes how a ball thrown horizontally or at an angle will follow a parabolic curve. This is due to the constant acceleration of gravity acting vertically while the horizontal velocity remains constant.

💡Acceleration

Acceleration in the context of the video refers to the rate of change of velocity of an object with respect to time. It is constant in projectile motion due to gravity and always directed vertically downwards. The video explains that this constant acceleration is what causes the parabolic shape of the projectile's path.

💡Velocity

Velocity is a vector quantity that refers to the speed of an object in a specific direction. The video emphasizes that velocity is always tangent to the curve of the projectile's path. It is constant in the horizontal direction when an object is projected horizontally, but it changes in the vertical direction due to gravity.

💡Horizontal Motion

Horizontal motion is the component of projectile motion that occurs along the horizontal plane. The video explains that in the absence of air resistance, an object in projectile motion will maintain a constant horizontal velocity, which can be described by the equation distance equals speed times time.

💡Vertical Motion

Vertical motion is the component of projectile motion that occurs along the vertical plane. The video discusses how vertical motion can be analyzed separately from horizontal motion, with the initial vertical speed often being zero for horizontal projections or non-zero for angled projections.

💡Air Resistance

Air resistance is the force that opposes the motion of an object through the air. The video mentions that for the purposes of calculation, air resistance is often considered negligible in basic projectile motion problems, simplifying the analysis to only consider the force of gravity.

💡Kinematics Equations

Kinematics equations are formulas used to describe the motion of an object. The video explains how different kinematics equations can be applied to analyze the horizontal and vertical components of projectile motion, such as the equations for constant velocity (distance = speed * time) and constant acceleration (v = u + at).

💡Gravity

Gravity is the force of attraction by the Earth that gives weight to physical objects. In the video, gravity is described as the constant acceleration that acts vertically downwards on an object in projectile motion, causing the object to follow a parabolic path.

💡Cliff

A cliff is used as a scenario in the video to illustrate projectile motion. The example involves throwing a ball horizontally from the edge of a cliff, which helps to visualize how the ball's path will be influenced by gravity, resulting in a parabolic trajectory.

💡Angle Theta

Angle Theta (θ) is the angle at which an object is projected relative to the horizontal. The video uses this term to explain how the initial velocity of a projectile can be resolved into horizontal and vertical components, which is crucial for analyzing the motion in two dimensions.

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 v² =

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