2-D Falling Bodies.

2-D Falling Bodies

Recall the formula for a constant acceleration…

Recall the formula for the distance a body travels when

it starts from rest, and

it starts from rest, and acceleration is constant

it does not start from rest

it does not start from rest the acceleration is constant

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.

vi =

vi = 0 m/s

vi = 0 m/s a =

vi = 0 m/s a = g =

vi = 0 m/s a = g = -9.80m/s2

What is the final velocity?

How far does a body fall?

How long does a body take to fall?

How Far?

How Far? Speed at bottom? (vf)

How Far? Speed at bottom? (vf) Time to fall?

Case Two:

Case Two: A body thrown up in the air

timeup =

timeup = timedown

timeup = timedown a =

timeup = timedown a = -9.80m/s2

timeup = timedown a = -9.80m/s2 vf =

timeup = timedown a = -9.80m/s2 vf = 0m/s (at the TOP!)

How long does it take to reach the top?

How long does it take to reach the top? -9.80m/s2

How long does it take to reach the top?

How high does it go?

How high does it go? substitute time

How high does it go?

How long to rise?

How long to rise? How high does it go?

Case Three:

Case Three: A body thrown sideways

Case Three: view from above…

Case Three: view from above… constant velocity

* the ball falls as if it was jut dropped

This diagram can be broken down into two simultaneous motions.

Horizontal motion -

Horizontal motion - constant velocity

Horizontal motion - dx = vxt constant velocity

Vertical motion -

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:

2-D Falling Bodies.

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2-D Falling Bodies.

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