1. Vertical Motion
Free Fall

2. Thought Exercise Describe the motion you see
Describe the object’s displacement, and how it changes, during the motion
Describe the object’s velocity, and how it changes, during the motion
Describe the object’s acceleration, and how it changes, during the motion
At what point during the motion is the object in “free fall”?

3. Free Fall
All objects moving under the influence of gravity only are said to be in free fall
Free fall does not depend on the object’s original motion
All objects falling near the earth’s surface fall with a constant acceleration
The acceleration is called the acceleration due to gravity, and indicated by g
Kinematic equations apply!
Use y for displacement
Use g for acceleration

4. Free Fall
Ball Dropped
Ball Thrown Down
vo= 0
a = g
vo< 0
a = g

5. Free Fall
Ball Thrown Upward
v = 0
v = 0
a = g
v > 0
a = g

6. If motion is symmetrical: tup = tdown vf = ‒ v0
Ball Thrown Upward
If motion is symmetrical: tup = tdown vf = ‒ v0

7. Group Exercise
A student throws a 250-gram ball upward with an initial velocity of 2.50 m/s.
What will be its maximum height from its point of release?
0.319 m
The student catches the ball at the same height from which it was thrown. What is its velocity when the student catches it?
‒2.50 m/s

8. Non-symmetrical Free Fall
Need to divide the motion into segments
Possibilities include
Upward and downward portions
The symmetrical portion back to the release point and then the non-symmetrical portion

9. Practice
A stone is thrown from the top of a building with an initial velocity of 20.0m/s straight upward, at an initial height of 50.0m above the ground. The stone just misses the edge of the roof on its way down.
Determine
a) time needed for the stone to reach maximum height
b) maximum height
c) time needed for stone to return to the height from which it was thrown; velocity at that point
d) velocity and position of the stone at 5.0s

10. Combination Motions

11. Practice
A rocket moves straight upward, starting from rest with an acceleration of +29.4m/s2. It runs out of fuel at the end of 4.00s and continues to coast upward, reaching a maximum height before falling back to Earth.
A) Find the rockets velocity and position at the end of 4.00s
B) Find the maximum height the rocket reaches
C) Find the velocity the instant before the rocket crashes on the ground