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Introduction to Projectile Motion. Mr. Chin-Sung Lin. Introduction to Projectile Motion. What is Projectile Motion?. Trajectory of a Projectile. Calculation of Projectile Motion. Introduction to Projectile Motion. What is Projectile Motion?. Trajectory of a Projectile.

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Introduction to projectile motion
Introduction toProjectile Motion

Mr.Chin-Sung Lin


Introduction to projectile motion1
Introduction to Projectile Motion

  • What is Projectile Motion?

  • Trajectory of a Projectile

  • Calculation of Projectile Motion


Introduction to projectile motion2
Introduction to Projectile Motion

  • What is Projectile Motion?

  • Trajectory of a Projectile

  • Calculation of Projectile Motion



Features of projectile motion
Features of Projectile Motion?

Thrown into the Air

2-D Motion

Parabolic Path

Affected by Gravity

Determined by Initial Velocity


Definition projectile motion
Definition: Projectile Motion

Projectile motion refers to the 2-D motion of an object that is given an initial velocity and projected into the air at an angle.

The only force acting upon the object is gravity. It follows a parabolic path determined by the effect of the initial velocity and gravitational acceleration.


Definition projectile motion1
Definition: Projectile Motion

Projectile motion refers to the 2-D motion of an object that is given an initial velocity and projected into the air at an angle.

The only force acting upon the object is gravity. It follows a parabolic path determined by the effect of the initial velocity and gravitational acceleration.


Introduction to projectile motion3
Introduction to Projectile Motion

  • What is Projectile Motion?

  • Trajectory of a Projectile

  • Calculation of Projectile Motion




y

v0

x


y

x


y

x


y

x


y

  • Velocity is changing and the motion is accelerated

  • The horizontal component of velocity (vx) is constant

  • Acceleration from the vertical component of velocity (vy)

  • Acceleration due to gravity is constant, and downward

  • a = - g = - 9.81m/s2

g = 9.81m/s2

x


y

  • The horizontal and vertical motions are independent of each other

  • Both motions share the same time (t)

  • The horizontal velocity ....vx = v0

  • The horizontal distance .... dx = vx t

  • The vertical velocity ........ vy = - g t

  • The vertical distance ........ dy = 1/2 gt2

g = 9.81m/s2

x


Trajectory path of a projectile2
Trajectory (Path) of a Projectile

  • The path of a projectile is the result of the simultaneous effect of the H & V components of its motion

  • H component  constant velocity motion

  • V component  accelerated downward motion

  • H & V motions are independent

  • H & V motions share the same time t

  • The projectile flight time t is determined by the V component of its motion


Trajectory path of a projectile3
Trajectory (Path) of a Projectile

  • H velocity is constant vx = v0

  • V velocity is changing vy = - g t

  • H range: dx = v0 t

  • V distance: dy = 1/2 gt2


Introduction to projectile motion4
Introduction to Projectile Motion

  • What is Projectile Motion?

  • Trajectory of a Projectile

  • Calculation of Projectile Motion


Calculation of projectile motion

v0

d

g

t

R

Calculation of Projectile Motion

  • Example: A projectile was fired with initial velocity v0horizontally from a cliff d meters above the ground. Calculate the horizontal range R of the projectile.


Strategies of solving projectile problems

v0

d

g

t

R

Strategies of Solving Projectile Problems

  • H & V motions can be calculated independently

  • H & V kinematics equations share the same variable t


Strategies of solving projectile problems1

v0

d

g

t

R

Strategies of Solving Projectile Problems

H motion: dx = vx t R = v0 t

V motion: dy = d = 1/2 gt2 t =sqrt(2d/g)

So, R = v0 t = v0 * sqrt(2d/g)


Numerical example of projectile motion
Numerical Example of Projectile Motion

H motion: dx = vx t R = v0 t = 10 t

V motion: dy = d = 1/2 gt2 t =sqrt(2 *19.62/9.81) = 2 s

So, R = v0 t = v0 * sqrt(2d/g) = 10 * 2 = 20 m

V0 = 10 m/s

g = 9.81 m/s2

19.62 m

t

R


Exercise 1 projectile problem

V0 = 10 m/s

g = 9.81 m/s2

d

t

20 m

Exercise 1: Projectile Problem

A projectile was fired with initial velocity 10 m/s horizontally from a cliff. If the horizontal range of the projectile is 20 m, calculate the height d of the cliff.


Exercise 1 projectile problem1

V0 = 10 m/s

g = 9.81 m/s2

d

t

20 m

Exercise 1: Projectile Problem

H motion: dx = vx t 20 = v0 t = 10 t t = 2 s

V motion: dy = d = 1/2 gt2 = 1/2 (9.81)22 = 19.62 m

So, d = 19.62 m


Exercise 2 projectile problem

V0

g = 9.81 m/s2

19.62 m

t

20 m

Exercise 2: Projectile Problem

A projectile was fired horizontally from a cliff 19.62 m above the ground. If the horizontal range of the projectile is 20 m, calculate the initial velocity v0 of the projectile.


Exercise 2 projectile problem1

V0

g = 9.81 m/s2

19.62 m

t

20 m

Exercise 2: Projectile Problem

H motion: dx = vx t 20 = v0 t

V motion: dy = d = 1/2 gt2 t =sqrt(2 *19.62/9.81) = 2 s

So, 20 = v0 t = 2 v0 v0 = 20/2 = 10 m/s


Summary of projectile motion
Summary of Projectile Motion

  • What is Projectile Motion?

  • Trajectory of a Projectile

  • Calculation of Projectile Motion



Example projectile problem h v
Example: Projectile Problem – H & V

A projectile was fired from ground with 20 m/s initial velocity at 60-degree angle. What’s the horizontal and vertical components of the initial velocity?

g = 9.81 m/s2

20 m/s

vy

60o

vx


Example projectile problem at the top
Example: Projectile Problem – At the Top

A projectile was fired from ground with 20 m/s initial velocity at 60-degree angle. What’s the velocity of the projectile at the top of its trajectory?

v

g = 9.81 m/s2

20 m/s

vy

t

60o

vx

R


Example projectile problem height
Example: Projectile Problem – Height

A projectile was fired from ground with 20 m/s initial velocity at 60-degree angle. What’s the maximum height that the ball can reach?

g = 9.81 m/s2

20 m/s

vy

h

60o

vx


Example projectile problem time
Example: Projectile Problem - Time

A projectile was fired from ground with 20 m/s initial velocity at 60-degree angle. How long will the ball travel before hitting the ground?

g = 9.81 m/s2

20 m/s

vy

t

60o

vx


Example projectile problem h range
Example: Projectile Problem – H Range

A projectile was fired from ground with 20 m/s initial velocity at 60-degree angle. How far will the ball reach horizontally?

g = 9.81 m/s2

20 m/s

vy

60o

vx

R


Example projectile problem final v
Example: Projectile Problem – Final V

A projectile was fired from ground with 20 m/s initial velocity at 60-degree angle. What’s the final velocity of the projectile right before hitting the ground?

g = 9.81 m/s2

20 m/s

vy

60o

vfx

vx

vfy

vf


Example projectile problem max r
Example: Projectile Problem – Max R

A projectile was fired from ground with 20 m/s initial velocity. How can the projectile reach the maximum horizontal range? What’s the maximum horizontal range it can reach?

g = 9.81 m/s2

20 m/s

q

R