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2-D Falling Bodies
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Recall the formula for a constant acceleration…
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Recall the formula for a constant acceleration…
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Recall the formula for the distance a body travels when
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Recall the formula for the distance a body travels when
it starts from rest, and
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Recall the formula for the distance a body travels when
it starts from rest, and acceleration is constant
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Recall the formula for the distance a body travels when
it starts from rest, and acceleration is constant
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Recall the formula for the distance a body travels when
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Recall the formula for the distance a body travels when
it does not start from rest
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Recall the formula for the distance a body travels when
it does not start from rest the acceleration is constant
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Recall the formula for the distance a body travels when
it does not start from rest the acceleration is constant
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Recall the formula for the distance a body travels when
it does not start from rest the acceleration is constant
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We will use these three formulae…
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We will use these three formulae…
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We will use these three formulae…
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We will use these three formulae…
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We also need to know the acceleration due to gravity.
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Case One:
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Case One: A body in free fall.
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Case One: A body in free fall.
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Case One: A body in free fall.
vi =
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Case One: A body in free fall.
vi = 0 m/s
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Case One: A body in free fall.
vi = 0 m/s a =
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Case One: A body in free fall.
vi = 0 m/s a = g =
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Case One: A body in free fall.
vi = 0 m/s a = g = -9.80m/s2
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Case One: A body in free fall.
What is the final velocity?
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Case One: A body in free fall.
What is the final velocity?
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Case One: A body in free fall.
What is the final velocity?
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Case One: A body in free fall.
What is the final velocity?
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Case One: A body in free fall.
What is the final velocity?
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Case One: A body in free fall.
What is the final velocity?
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Case One: A body in free fall.
How far does a body fall?
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Case One: A body in free fall.
How far does a body fall?
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Case One: A body in free fall.
How long does a body take to fall?
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Case One: A body in free fall.
How long does a body take to fall?
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Case One: A body in free fall.
How long does a body take to fall?
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Case One: A body in free fall.
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Case One: A body in free fall.
How Far?
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Case One: A body in free fall.
How Far?
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Case One: A body in free fall.
How Far? Speed at bottom? (vf)
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Case One: A body in free fall.
How Far? Speed at bottom? (vf)
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Case One: A body in free fall.
How Far? Speed at bottom? (vf) Time to fall?
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Case One: A body in free fall.
How Far? Speed at bottom? (vf) Time to fall?
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Case Two:
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Case Two: A body thrown up in the air
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Case Two: A body thrown up in the air
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Case Two: A body thrown up in the air
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Case Two: A body thrown up in the air
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Case Two: A body thrown up in the air
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Case Two: A body thrown up in the air
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Case Two: A body thrown up in the air
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Case Two: A body thrown up in the air
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Case Two: A body thrown up in the air
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Case Two: A body thrown up in the air
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Case Two: A body thrown up in the air
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Case Two: A body thrown up in the air
timeup =
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Case Two: A body thrown up in the air
timeup = timedown
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Case Two: A body thrown up in the air
timeup = timedown a =
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Case Two: A body thrown up in the air
timeup = timedown a = -9.80m/s2
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Case Two: A body thrown up in the air
timeup = timedown a = -9.80m/s2 vf =
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Case Two: A body thrown up in the air
timeup = timedown a = -9.80m/s2 vf = 0m/s (at the TOP!)
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Case Two: A body thrown up in the air
How long does it take to reach the top?
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Case Two: A body thrown up in the air
How long does it take to reach the top?
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Case Two: A body thrown up in the air
How long does it take to reach the top?
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Case Two: A body thrown up in the air
How long does it take to reach the top?
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Case Two: A body thrown up in the air
How long does it take to reach the top?
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Case Two: A body thrown up in the air
How long does it take to reach the top?
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Case Two: A body thrown up in the air
How long does it take to reach the top?
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Case Two: A body thrown up in the air
How long does it take to reach the top?
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Case Two: A body thrown up in the air
How long does it take to reach the top? -9.80m/s2
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Case Two: A body thrown up in the air
How long does it take to reach the top?
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Case Two: A body thrown up in the air
How long does it take to reach the top?
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Case Two: A body thrown up in the air
How high does it go?
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Case Two: A body thrown up in the air
How high does it go?
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Case Two: A body thrown up in the air
How high does it go?
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Case Two: A body thrown up in the air
How high does it go?
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Case Two: A body thrown up in the air
How high does it go?
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Case Two: A body thrown up in the air
How high does it go?
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Case Two: A body thrown up in the air
How high does it go?
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Case Two: A body thrown up in the air
How high does it go?
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Case Two: A body thrown up in the air
How high does it go?
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Case Two: A body thrown up in the air
How high does it go? substitute time
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Case Two: A body thrown up in the air
How high does it go?
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Case Two: A body thrown up in the air
How long to rise?
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Case Two: A body thrown up in the air
How long to rise?
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Case Two: A body thrown up in the air
How long to rise? How high does it go?
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Case Two: A body thrown up in the air
How long to rise? How high does it go?
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Case Three:
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Case Three: A body thrown sideways
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Case Three: A body thrown sideways
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Case Three: A body thrown sideways
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Case Three: A body thrown sideways
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Case Three: A body thrown sideways
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Case Three: A body thrown sideways
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Case Three: A body thrown sideways
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Case Three: A body thrown sideways
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Case Three: A body thrown sideways
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Case Three: A body thrown sideways
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Case Three: A body thrown sideways
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Case Three: A body thrown sideways
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Case Three: A body thrown sideways
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Case Three: A body thrown sideways
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Case Three: A body thrown sideways
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Case Three: view from above…
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Case Three: view from above…
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Case Three: view from above…
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Case Three: view from above…
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Case Three: view from above…
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Case Three: view from above…
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Case Three: view from above… constant velocity
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Case Three: A body thrown sideways
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Case Three: A body thrown sideways
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Case Three: A body thrown sideways
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Case Three: A body thrown sideways
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Case Three: A body thrown sideways
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Case Three: A body thrown sideways
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Case Three: A body thrown sideways
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Case Three: A body thrown sideways
* the ball falls as if it was jut dropped
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Case Three: A body thrown sideways
This diagram can be broken down into two simultaneous motions.
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Case Three: A body thrown sideways
Horizontal motion -
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Case Three: A body thrown sideways
Horizontal motion -
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Case Three: A body thrown sideways
Horizontal motion - constant velocity
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Case Three: A body thrown sideways
Horizontal motion - dx = vxt constant velocity
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Case Three: A body thrown sideways
Vertical motion -
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Case Three: A body thrown sideways
Vertical motion -
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Case Three: A body thrown sideways
Vertical motion – “just as if dropped”
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Case Three: A body thrown sideways
Vertical motion – “just as if dropped”
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Case Three: A body thrown sideways
Vertical motion – “just as if dropped”
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Kinematics in 2-D (p106) When on object is thrown in the air, it is a projectile. When an object is thrown horizontally through the air it moves in 2 directions (dimensions): horizontally & vertically The horizontal components are in the “x” direction: vx and dx The vertical components are in the “y” direction: vy and dy
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(p 106) the horizontal motion is uniform motion and the equation is:
The vertical motion is uniform accelerated motion and can be described by the equations: Start each 2-D problem with a labeled diagram and use the following strategy (add to p 107):
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Vertical Horizontal 1st find time 2nd use time to find:
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Modify Example on p 107 (add-Remember horizontal and vertical motion are independent of each other!). Diagram:
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