Gravity & Falling Objects
Kinematics Unit
Kinematics Problems
You’ll be given problems that may use any
of the formulas or their variations for a
solution.
Useful strategies:
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Read and attempt to visualize problem
Identify given quantities
Identify unknown quantities
Select formula with given and unknown quantities
Make certain acceleration is constant
Manipulate formula if needed
Substitute variables
Falling Objects
When an object is dropped, it picks up speed
as it falls. Why?
 This is acceleration produced by gravity.
All things fall to earth with a constant
acceleration regardless of mass.
Ignoring air resistance, the acceleration
due to gravity is the same for all objects at
the same location on earth.
Let’s see this phenomenon:
https://www.youtube.com/watch?v=E43CfukEgs
Acceleration due to gravity is given the
symbol g, with a magnitude of 9.81 m/s2.
 This value does change depending on the
elevation above sea level. However, we will
ignore it because it’s not noticeable unless you
are on a mountaintop.
Acceleration is a vector; therefore, we choose
up as our positive direction.
Thus, g is – 9.8 m/s2 since gravity pulls things
downwards.
We can use the 4 kinematics equations to
solve all problems involving the motion of
falling objects.
There are 2 cases: (1) freely falling objects and
(2) objects initially thrown upwards.
Case 1: Freely falling objects
Eg. 1 At Playland, the Hellevator freely falls for
1.5 s. What is its velocity at the end of this time?
How far does it fall?
v f = vi + gt
t = 1.5 s
vi = 0
a = g = – 9.8 m/s2
vf = ?
d=?
m
= 0 + (-9.8 2 )(1.5s)
s
m
m
= -14.7 » -15
s
s
1 2
d = vi t + gt
2
1
m
2
= (0)(1.5s) + (-9.8 2 )(1.5s)
2
s
= -11.025m » -11m
Case 2: Objects initially thrown upwards
 These properties are always true:
a) The instantaneous velocity at the
highest point the object reaches is
zero.
b) tup = tdown
c) The velocity of the object when it
returns to the point at which it was
released is the same as its initial
velocity but in the opposite
(negative) direction.
d) The acceleration due to gravity is
always in the downwards (negative
direction).
Eg. 2 A tennis ball is thrown straight up with
an initial velocity of 22 m/s. It is caught at the
same distance above ground from which it
was thrown. How high does the ball rise?
Consider either trip up or trip down.
a = g = – 9.8 m/s2
vi = 22 m/s
vf = 0
d=?
v 2f = vi2 + 2ad
v 2f - vi2
d=
2a
m 2
)
s
=
m
2(-9.8 s )
s
0 - (22
= 24.694m » 25m
 Eg. 3 (more challenging!) The tennis ball in Eg. 2 is
thrown upward while being held over the edge of
a cliff 30 m high. It is not caught and proceeds to
fall off the cliff and to the ground. What is its
velocity right before it hits the ground? For how
long is it in the air?
On whiteboard
Terminal Velocity
 Objects accelerate downward continuously due to
gravity.
 An object in free fall accelerates until it reaches its
terminal velocity – the point at which it no longer
speeds up and travels at a constant velocity.
 This occurs because air friction increases as the
object speeds up. Once air friction equals the force
of gravity, it can no longer accelerate.
Homework
 First Kinematics Worksheet #4 and 8
 Second Kinematics worksheet – Vertical Motion
problems