Projectile motion
This presentation is the property of its rightful owner.
Sponsored Links
1 / 32

Projectile Motion PowerPoint PPT Presentation


  • 108 Views
  • Uploaded on
  • Presentation posted in: General

Projectile Motion. Chapter 3.3. Objectives. Recognize examples of projectile motion Describe the path of a projectile as a parabola Resolve vectors into their components and apply the kinematic equations to solve problems involving projectile motion. Projectile Motion.

Download Presentation

Projectile Motion

An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

Presentation Transcript


Projectile motion

Projectile Motion

Chapter 3.3


Objectives

Objectives

  • Recognize examples of projectile motion

  • Describe the path of a projectile as a parabola

  • Resolve vectors into their components and apply the kinematic equations to solve problems involving projectile motion


Projectile motion1

Projectile Motion

  • How can you know the displacement, velocity and acceleration of a ball at any point in time during its flight?

  • Use the kinematic equations of course! 


Vector components p 98 running vs jumping

Vector Components p.98 (Running vs Jumping)

While running, the person is only moving in one dimension

Therefore, the velocity only has one component.

V

While jumping, the person is moving in two dimensions

Therefore, the velocity has two components.

Vy

Vx


Definition of projectile motion

Definition of Projectile Motion

  • Objects that are thrown or launched into the air and are subject to gravity are called projectiles

  • Examples?

    • Thrown Football, Thrown Basketball, Long Jumper, etc


Path of a projectile

Path of a projectile

  • Neglecting air resistance, the path of a projectile is a parabola

  • Projectile motion is free fall with an initial horizontal velocity

  • At the top of the parabola, the velocity is not 0!!!!!!


Vertical and horizontal motion

Vertical and Horizontal Motion


Equations for projectiles launched horizontally

Equations for projectiles launched horizontally


Revised kinematic eqns for projectiles launched horizontally

Revised Kinematic Eqns for projectiles launched horizontally


Finding the total velocity

V

Vy

Vx

Finding the total velocity

  • Use the pythagorean theorem to find the resultant velocity using the components (Vx and Vy)

  • Use SOH CAH TOA to find the direction


Example p 102 2

Example p. 102 #2

  • A cat chases a mouse across a 1.0 m high table. The mouse steps out of the way and the cat slides off the table and strikes the floor 2.2 m from the edge of the table. What was the cat’s speed when it slid off the table?


What do we know and what are we looking for

Vx= ?????

What do we know and what are we looking for?

Δx= 2.2 m

Δy= -1.0m (bc the cat falls down)

What are we looking for??

1.0 m

2.2m


How do we find vx

How do we find Vx?

  • Equation for horizontal motion:

  • We have x…so we need t.

  • How do we find how long it takes for the cat to hit the ground?

  • Use the vertical motion kinematic equations.


Vertical motion

Vertical Motion

  • Δy= -1.0m

  • a=-9.81 m/s^2

  • What equation should we use?

  • Rearrange the equation, to solve for t then plug in values.


Horizontal equation

Horizontal equation

  • Rearrange and solve for Vx:

  • Cat’s Speed is 4.89 m/s


Cliff example

Cliff example

  • A boulder rolls off of a cliff and lands 6.39 seconds later 68 m from the base of the cliff.

    • What is the height of the cliff?

    • What is the initial velocity of the boulder?


How high is the cliff

How high is the cliff?

  • Δy= ?a=-9.81 m/s2

  • t = 6.39 sVx=?

  • Vy,i = 0 Δx= 68 m

The cliff is 200 m high


What is the initial velocity of the boulder

What is the initial velocity of the boulder?

  • The boulder rolls off the cliff horizontally

  • Therefore, we are looking for Vx


Important concepts for projectiles launched horizontally

Important Concepts for Projectiles Launched Horizontally


Projectiles launched at an angle

Vi

Vi = Vx

Vy,i

θ

Vx,i

Projectiles Launched at An Angle


Components of initial velocity for projectiles launched at an angle

Vi

Vy,i

θ

Vx,i

Components of Initial Velocity for Projectiles Launched at an angle


Revise the kinematic equations again

Revise the kinematic equations again


Example p 104 3

Example p. 104 #3

  • A baseball is thrown at an angle of 25° relative to the ground at a speed of 23.0 m/s. If the ball was caught 42.0 m from the thrower, how long was it in the air? How high was the tallest spot in the ball’s path?


What do we know

25°

42.0 m

What do we know?


What can we use to solve the problem

What can we use to solve the problem?

Find t using the horizontal eqn:

Δx=vxΔt = vicos(θ)t

  • How to find Δy?

    • Vy,f = 0 at top of the ball’s path

    • What equation should we use?


Cliff example1

Cliff example

  • A girl throws a tennis ball at an angle of 60°North of East from a height of 2.0 m. The ball’s range is 90 m and it is in flight for 6 seconds.

    • What is the initial horizontal velocity of the ball?

    • What is the initial vertical velocity of the ball?

    • What is the total initial velocity of the ball?

    • How high above the initial position does the ball get?

    • What is the vertical velocity of the ball 2 seconds after it is thrown?


What is the initial horizontal velocity of the ball

What is the initial horizontal velocity of the ball?

  • Δx= 90 m

  • Θ=60°

  • Total time= 6 s

  • Horizontal velocity is constant: Vx


What is the initial vertical velocity of the ball

Vi

Vy,i

θ

Vx,i

What is the initial vertical velocity of the ball?


What is the total initial velocity of the ball

Vi

Vy,i

θ

Vx,i

What is the total initial velocity of the ball?


How high above the ground does the ball get

How high above the ground does the ball get?

  • At the top of the parabola, Vy is 0…so use the revised kinematic equations

  • Add 2m to get the height above the ground: 36.65 m


What is the vertical velocity of the ball 2 seconds after it is thrown

What is the vertical velocity of the ball 2 seconds after it is thrown?

  • Vy,i=+26 m/s

  • a= -9.81 m/s2

  • t = 2 seconds


Important concepts for projectiles launched at an angle

Important Concepts for Projectiles Launched at an Angle

  • At the top of the parabola, neither the object’s velocity nor it’s acceleration is 0!!!!!

    • Only Vy is 0

    • Vx is constant throughout the flight

    • Horizontal acceleration is always 0

    • Vertical acceleration is always -9.81 m/s2


  • Login