Projectile Motion
Projectiles (vertical, horizontal and at an angle)
Vertical Kinematics
Freefall
Kinematics

Remember our three kinematics:
 a = (vf-vi)
t
 ∆ d = vit + (1/2)at2
 vf2 = vi2 + 2a∆d
Freefall

Freefall refers to when an object is falling
in air with no air resistance.
◦ Obviously, there is air resistance in the real
world. We will not take that into account
when performing our calculations. All of our
problems will take place in a vacuum 

Objects in freefall are constantly
accelerated at a rate of -9.8 m/s2. This
number is equal to the acceleration due
to gravity.
Specific conditions

When an object is dropped:
◦ Initial velocity is equal to zero.
◦ Final velocity is the velocity before the object
hits whatever it will hit, so it is NOT zero.
◦ Final velocity, acceleration, and displacement will
always be negative because the object is traveling
downward. Time is always positive.
 You may be complicated and set your coordinate plane
such that downward = positive and upward = negative.
This will reverse the signs for final velocity, acceleration,
and displacement. If you do this, WRITE OUT YOUR
GIVENS AND SHOW YOUR WORK.
Diagramming the problem
Practice

The observation deck of tall skyscraper
370 m above the street. Determine the
time required for a penny to free fall from
the deck to the street below.

A stone is dropped into a deep well and
is heard to hit the water 3.41 s after
being dropped. Determine the depth of
the well.
Specific conditions (cont.)

When an object is thrown:
◦ The problem must be split in HALF, the trip
up and the trip down.
◦ Conditions will be different dependent on
which half you are solving for:
 The way down will be like normal freefall
 The way up will have a positive initial velocity and
displacement, and final velocity will be equal to zero.
Acceleration is still negative, and never equal
to zero.
Diagramming the problem
Practice

A kangaroo is capable of jumping to a height of
2.62 m. Determine the takeoff speed of the
kangaroo.

A baseball is popped straight up into the air and
has a hang-time of 6.25 s. Determine the height
to which the ball rises before it reaches its peak.
(Hint: the time to rise to the peak is one-half the
total hang-time.)

If Michael Jordan has a vertical leap of 1.29 m,
then what is his takeoff speed and his hang time
(total time to move upwards to the peak and
then return to the ground)?
Assignment (Application of
Content)

Individually complete #45-46 on p.74

Complete the worksheet about Free Fall
Problems.

When all work is completed, we’ll head in
the lab for a short vertical projectile lab.
Horizontal Projectiles
x and y kinematics
Chapter 6, section 1
p.147-152
The basics

X-direction: vx =
x/t
◦ Velocity is constant, so ax = 0

y-direction: conditions for dropped free
fall is true
Diagramming the problem
Practice problem

At practice, coach Creasy decided to do
tackling drills on a cliff. PJ was the
unfortunate victim of his rage, and he was
tackled horizontally off the cliff at 3.0 m/s
and travels 9.0 m horizontally from the
base of the cliff. Determine the height of
the cliff.
One more practice problem

The coyote runs horizontally off the cliff
with a speed of 5 m/s and plunges 250 m
to the ground below. What was the
coyote’s final velocity (magnitude and
direction)?
Book practice

Practice p.150 #1-3
Angled Projectiles
x, y, and angles (right triangles and vectors)
Projectiles at an angle
X-direction is still the same!
 Y-direction changes from dropped freefall
to thrown free fall.


In this case, objects are thrown at an
angle, not straight up like in the freefall
problems.
◦ This means we’ll need….VECTORS!
How to start a problem



Read and write down all givens. Assign them
the correct variable. Write out all formulas.
Draw a picture. Include a beginning right
triangle and an ending right triangle.
SOLVE FOR TIME!
◦ Remember that time connects the x and y
directions.

Solve the problem, one unknown at a time.
Look back at your givens and formulas each
time.
Here we go!
A friend and I, who happens to be exactly
my height, were casually tossing a
football. I threw it at an angle of 35o
above the horizontal with a velocity of
1.24 m/s. Find the following:
a)
b)
c)
d)
Horizontal velocity
Height that the football reached
Total time that the ball was in the air
Final velocity (magnitude and direction)
Textbook practice

Open to page 152 and complete
problems 4 and 5.
Combined Angled off a Cliff
A gazelle jumps off of a 35 m high cliff. The
gazelle jumps with an initial velocity of 2.2
m/s at an angle of 53o with the horizontal.
Find the follwing:
a) Horizontal displacement
b) Height above the cliff that the gazelle
reached
c) Total time that the gazelle was in the air
d) Final velocity (magnitude and direction)
Textbook practice

Open to page 152 and complete problem
6.
vf = 32 m/s at 82o