Name
Date
Free Fall and Hang Time
In Regents Physics, we do not deal with air resistance mathematically (only
conceptually). Due to this, the only force acting on an object thrown or falling through the air
near a planet’s surface is the force due to gravity. This means the acceleration is straight
downward, toward the planet’s surface. Since this acceleration is a constant for the specific
planet, rather than using the symbol a, we use the symbol g. For Earth, this number is listed on
the front of the reference tables as ‘acceleration due to gravity’. The value of this constant is
9.8 m/s2 for Earth. On multiple choice questions, this value can be rounded to 10.
Free Fall:




When an object is dropped near a planet’s surface, gravity causes the object to fall
downward.
When this occurs, the object is said to be in ‘free fall’.
For problems like this, the object almost always starts from rest and goes downward.
Due to this, we can make downward the positive direction to make the math easier.
When the object is dropped, the vi is 0. This simplifies two of our equations:
o
= + becomes =
o

=
+
becomes
=
(though the distance is usually the height h)
For Earth (and rounding 9.8 to 10), this gives us some specific numbers based on the time
of flight.
Elapsed time (s)
0
1
2
3
4
5
t
Instantaneous
speed (m/s)
0
10
20
30
40
50
10t
Distance fallen (m)
0
5
20
45
80
125
5t2
Objects Thrown Downwards:



For objects that are thrown downwards, the only difference from drop problems is your vi
is no longer zero.
For problems like this, you are usually solving for the distance or final speed.
Plug in the vi and g into the regular kinematics equations.
Air resistance and falling objects:



If you drop a feather and a coin, you’ll find that the coin reaches the floor way before the
feather.
The reason for this is not that two objects have different gravitational forces pulling on
them – it’s because there’s air resistance that keeps the feather up longer.
If all of the air were to be removed from the room (called a vacuum), the feather and the
coin will fall side by side at the acceleration g.
For objects thrown upwards (hang time):






Just like free fall problems, hang time problems have the acceleration straight down. The
velocity starts off straight up, becomes zero, and ends straight down.
The motion is split into two parts: when the object is going upwards, and when the object
is going downwards.
The downward part is exactly like a drop problem.
o At the top of the arc, the velocity (vtop) is zero with the acceleration down.
o So for problems where you are concerned with the distance and time, treating it
like a drop problem is the best course of action.
The upward part is like an object that is slowing down.
o The velocity (vup) is upwards and the acceleration is downwards.
o This means that if you use this part of the problem, either the acceleration or
velocity must be negative.
In class, I will almost always use the downwards part to make our lives easier.
One thing to keep in mind, the time it takes to go up (tup) and the time it takes to fall from
the top (tff) are equal.
o The total time (ttotal) is twice the time to fall.
t
vi
vf
d
a
Upwards
tup
vup upwards
0 m/s
h
-g
=
and
Downwards
tff
0 m/s
vup downwards
h
g
=2