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