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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.

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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!!!!!!
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 s Vx=?
  • 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
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 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
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
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