Physics

Free-fall with horizontal velocity
(assuming we ignore any effects of air resistance)

The curved path that an object follows when
thrown or launched near the surface of Earth
is called a trajectory

Projectiles follow perfect parabolic
trajectories when air resistance is
neglected…remember Δy is prop. to t2


Constant when air resistance is negligible
At any point in a projectile’s path, horizontal
velocity is the same initial horizontal velocity


Acceleration is a constant -9.81 m/s2
At the peak of a projectile’s path, vertical
velocity is zero

The horizontal and vertical components of
motion are completely independent of one
another.
•The velocity at any point along the trajectory is just the
vector sum of the horizontal and vertical components
•The instantaneous direction is tangent to the path at
any location
Horizontal
Motion
Vertical
Motion
Forces
(present? Yes or no?)
(if present, which
direction?
No
Yes
Downward
Acceleration
(present? Yes or no?)
(if present, which
direction?
No
Yes
Downward
Constant
Changing
Velocity
(constant or changing)
a. Determine how much time it takes to fall.
b. Determine how far from the base of the cliff
it is when it hits the ground.
c. Determine how fast it is moving vertically
when it hits the ground.
d. Determine what its total velocity is when it
hits the ground.

Determine the initial horizontal velocity of the
soccer ball.

How far downrange will the bullet hit the
ground?
Physics 2010
The launch velocity
of the projectile
needs to be split up
into its component
parts for analysis
purposes.
Note: the initial
vertical velocity
is no longer
zero!!!
Initial
velocity
analysis:
V
Vyi = V sinθ
Vx = Vcosθ
These values can now
be used in the
kinematic equations…
a. How high will it go?
b. How much time does it spend in the air?
c. How far away from you will it hit the ground?
d. What is the ball’s velocity when it hits the
ground?
a. Find the range of the ball.
b. Find the maximum height of the ball.
a. Find its “hang time” (time that the ball is in
the air).
b. Find the distance the ball travels before it
hits the ground.
c. Find its maximum height.



One dimensional motion equations still apply.
You will need to resolve the initial velocity
into its x- and y-components to separate the
horizontal from the vertical motion.
Always keep the horizontal information
separate from the vertical information in the
problem.

Find its position and velocity after 8.00 s.

Find the time required to reach its maximum
height.

Find the range of the projectile.