Transcript 2-D Motion (Projectile motion) PPT.ppt

What is Projectile
Motion?
Projectile Motion
• A projectile is an object moving in two
dimensions under the influence of
Earth's gravity
• Two-dimensional motion of an object
– Vertical
– Horizontal
Types of Projectile
Motion
• Horizontal
– Motion of a ball rolling freely along
a level surface
– Horizontal velocity is ALWAYS
constant
• Vertical
– Motion of a freely falling object
– Force due to gravity
– Vertical component of velocity
changes with time
• Parabolic
– Path traced by an object
accelerating vertically while moving
horizontal
3-7 Projectile Motion
Are the same
It can be understood
by studying the
horizontal and vertical
motions separately.
velocity vector
Path of object
velocity components
Examples of Projectile
Motion
• Launching a Cannon ball
The speed in the x-direction is constant;
in the y-direction the object moves with
constant acceleration (g) because of
gravity.
THE COMPONENTS
• Vertical
– Velocity decreases on
the way up and
increases on the way
down (free fall)
– And at the top of its
path, velocity is what?
– Acceleration is the same
up and down when you
reach the same height
• Question:
– If you were walking at
a constant velocity with
a baseball and threw it
up in the air while you
were walking, would it
fall
a)In front of you
b)Behind you
c)Right back in your
hands
Solving Problems
Involving Projectile
Motion
Example: Where does the apple land?
A child sits upright in a wagon which is
moving to the right at constant speed as
shown. The child extends her hand and
throws an apple straight upward (from her
own point of view), while the wagon continues
to travel forward at constant speed.
If air resistance is neglected, will the apple
land
(a)behind the wagon
(b)in the wagon
(c)in front of the wagon?
TAKE HOME MESSAGE
• The X-velocity is independent of the Yvelocity
• The speed in the x-direction (horizontal)
doesn’t care what the speed in the ydirection (vertical) is!
• WHY?
REVIEW QUESTION
• Suppose two balls are released from the
same height:
– One is dropped from rest the other is thrown
horizontally. Which will hit the ground first?
Why?
Factors Affecting
Projectile Motion
• What two factors would affect projectile
motion?
– Angle
– Initial velocity
(height – y dist)
(range – x dist)
Initial Velocity
Angle
THE FACTORS
• Angle
– 0°- 45° = range
increases
– 45° - 90° = range
decreases
• Initial velocity
– Greater initial velocity=
farther it will go
– The faster it goes
horizontally, more
ground is covered
HORIZONTAL
EQUATIONS SYMBOLS
– dx= Horizontal displacement
(RANGE)
–vxi, vx = Horizontal velocity of a
projectile
VERTICAL EQUATIONS
SYMBOLS
• Symbols
–dy= vertical displacement (HEIGHT)
–g = acceleration of gravity (9.81 m/s²)
–Vyi = initial vertical velocity (m/s)
–Vyf = final vertical velocity (m/s)
–Vy = vertical velocity
Object Launched Horizontally
vx = initial horizontal velocity
dy = initial height
above ground
t = total time in the air
dx = horizontal range
IMPORTANT FACTS
There is no horizontal acceleration.
There is no initial vertical velocity.
The horizontal velocity is constant.
Time is the same for both vertical and horizontal.