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Projectile Motion. If you throw a javelin…. What affects it’s flight? Gravity How hard you throw it (initial velocity) What angle you throw it at Air resistance (shape of javelin) Mass Which one of these has no affect?. Let’s take a look at how they affect flight!.

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if you throw a javelin
If you throw a javelin…

What affects it’s flight?

  • Gravity
  • How hard you throw it (initial velocity)
  • What angle you throw it at
  • Air resistance (shape of javelin)
  • Mass

Which one of these has no affect?

let s take a look at how they affect flight
Let’s take a look at how they affect flight!

http://galileoandeinstein.physics.virginia.edu/more_stuff/Applets/ProjectileMotion/jarapplet.html

slide4

We call the arc of the javelin toss:

Projectile Motion

  • Projectiles travel along a curved trajectory
projectile motion1
Projectile Motion
  • A video introduction
what is a projectile
What is a Projectile?
  • Projectile

– an object that moves along a 2-D curved trajectory

- does not have any propulsion when in flight

  • Examples:
    • Football, baseball, tennis ball, etc
    • Bullets
    • Snow boarders in a half pipe
    • Cliff divers
did you notice
Did you notice?
  • The projectiles hit the ground at the same time regardless of horizontal velocity
  • Object accelerates downwards (at 9.81 m/s2 – acceleration due to gravity)
  • Horizontal displacement stays constant throughout motion
conclusions about projectile motion
Conclusions about Projectile motion
  • The horizontal component of a projectile’s velocity is constant (no acceleration)
  • Projectile experiences constant downwards acceleration (gravity)
  • Horizontal and vertical motion of a projectile are independent of each other (except they have a common time)
important variables
Important Variables
  • Time – Δt
  • Velocity – v
  • Height – Δdy
  • Distance – ΔdX
  • Acceleration – a
  • Launch Angle - θ
strategy to solving projectile motion problems
Strategy to Solving Projectile Motion Problems
  • Analyze horizontal motion and vertical motion independently
    • Separate the velocity vector into x- and y- components
  • Remember: Time is common between them
slide16

Horizontal motion:

- Constant velocity (0 accel.) in the x direction

- Equation : v = d/t

Vertical motion:

- Constant acceleration - 9.8 m/s2 [down]

- Use the accel. equations we used previously

slide17

Two Types of Problems:

One DimensionalProblems (no horiz. Velocity)

Case 1: Object dropped from rest

Case 2: Object thrown directly upwards

Two Dimensional Problems:

Case 3: Rolled over an edge

Case 4: Shot at an angle

Let’s analyze the four cases!

for two dimensional problems
For Two Dimensional Problems:

Break the initial velocity into horizontal and vertical components (using the given angle and trigonometry)

vy

θ

vx

slide21

Example Question (Case 3)

A tennis ball is rolled off a counter at 8 m/s, what will it’s position be after 3s?

Example Question (Case 4)

A golfer strikes a golf ball on level ground. The ball leaves the ground with an initial velocity of 42 m/s [32o above the horizontal].

a) What will the ball’s position be after 4 s?

b) What will be the maximum height attained?