Introduction to Projectile Motion
Thursday, November 20, 2014
Thursday, 11/20
Unit 5: Projectile Motion
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Pick up a handout from the ‘Physics bin’
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Make note of upcoming dates below.
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Respond to the following in the ‘warm-up’ section of your handout.
What roles do inertia and gravity have in an objects motion? Do they complement each
other or are they at odds with each other?
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Upcoming dates
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Monday, 11/24 thru Friday, 11/28 Thanksgiving holiday
Thursday, 12/4 – exemption window opens
Friday, 12/5 – Projectile motion quiz
Friday, 12/5 – Review due when the late bell rings
Tuesday, 12/9 – Projectile motion test
Wednesday, 12/10 – exemption window closes
Friday, 12/12 – 3SW extra credit due
Wednesday, 12/17 – 2nd period final: 8:35 am to 10:07 pm
Friday, 12/19 - 4th period final: 10:00 to 11:20 am
Friday, 12/19 – end of the semester
Real – life projectiles
Where we’ve been
•
Studied linear motion
• Motion in one direction
• Included motion in the x direction (horizontal
motion)and y direction (free fall)
Where we’re going
• Combine our understandings of linear motion and vectors
to describe and analyze a special kind of two dimensional
motion
• We will use diagrams, numbers, equations, and words for
describing and analyzing projectile motion.
Definitions
• Projectile – An object that is launched by a
force and continues to move by its own
inertia – it is only under the influence of
gravity
• Trajectory – the path of a projectile.
• Parabola – geometric shape of the path of
a projectile.
• Range – the total horizontal distance
traveled by a projectile
Projectile motion problems are solved by
treating horizontal and vertical motion separately.
*IMPORTANT*
Gravity only affects vertical
motion.
.
1. object launched horizontally
2. object launched at an angle
Objects Launched Horizontally
vi = initial horizontal velocity
dy = vertical
distance
t = total time in the air
(height)
dx = horizontal distance
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.
Equation
Δd = vi . t + ½ . a . t2
horizontal
dx = vi.t
vertical
dy = 1/2 . ag.t2
Object Launched at an Angle
vi = initial velocity
q = launch angle
q
t = total time in air
IMPORTANT FACTS
dx = horizontal range
• The horizontal velocity is constant.
• Gravity only effects the vertical motion.
• It rises and falls in equal time intervals.
• It reaches maximum height in half the total time.
• When at maximum height, vertical velocity is zero.
• Final vertical velocity is equal to
Negative initial vertical velocity
• Change in vertical position is zero (because it lands
at the same height it was launched from)
Structure for Problem Solving
• GUESS has not gone away it just looks a
little different.
G:
U:
Horizontal (x)
Vertical (y)
Δx
Δy
Vi
Vi
a
a
t
t
Structure for Problem Solving
(Cont.)
E:
S:
Substitute Variables
S:
Solve
Horizontal Projectile Knowns
Horizontal (x)
Vertical (y)
Δx (given or you will solve for it)
Δy (given or you will solve for it)
Vi (given or you will solve for it)
Vi = 0
A (constant velocity therefore 0)
a = 9.8 m/s2
t (given or you will solve for it)
t (given or you will solve for it)
Note: time will be the same for the horizontal and vertical. Why?
Example 1
A stone is thrown horizontally at 7.5 m/s from
a cliff that is 68.4 m high. How far from the
base of the cliff does the stone land?
G:
U:
E:
Horizontal (x)
Vertical (y)
Δx
Δy
Vi
Vi
a
a
t
t
Example 2
A baseball is thrown horizontally with a velocity of 44 m/s. It travels a horizontal
distance of 18 m to the plate before it is caught.
a.
b.
How long does the ball stay in the air?
How far does the ball drop during its flight?
G:
U:
E:
Horizontal (x)
Vertical (y)
Δx
Δy
Vi
Vi
a
a
t
t
Practice