GENERAL PHYSICS 1
M O D U L E 4
The following are the lessons contained in this module:
1. PROJECTILE MOTION: 2D MOTION
At the end of this module, you are expected to:
Describe motion using the concept of relative velocities in 1D and 2D
Deduce the consequences of the independence of vertical and horizontal components of
projectile motion;
Calculate the range, time of flight, and maximum height of projectiles.
Lesson 4
PROJECTILE MOTION
Projectile motion happens everywhere: a basketball being thrown on the ring, a piece of
crumpled paper being thrown on a garbage can, water from a hose being aimed at some plants,
and then some.
First, we need to discuss the proper definition of projectile motion. Projectile motion is
motion in two directions (horizontal and vertical) that are independent of each other and with
the vertical motion—gravity—the only force that is acting on it.
For a little bit of history, let’s have a brief review of the contributions of Galileo to the
concept of the projectile motion. He proposed that objects being thrown at different initial
orientation (either from the side, horizontally—or from ground up or downward, vertically) will
arrive at the ground at the same time. This was proven true but there are special environments
where this can be achieved at the smallest percentage of error: in a vacuum setting without any
air resistance. He also proposed that the vertical acceleration (because of the constant force
acting on projectile motions) always remain constant at 9.81 m/s2.
REMEMBER: Although this is true in reality, there is also air resistance in real life that
contributes to some misconceptions. This is why when asked if which arrives on the ground first,
a feather or a stone, the majority of the answer will be the stone. The stone will most likely reach
the ground first, but that’s only because air resistance made the feather’s flight to the ground
harder, having been thrown here and there.
EQUATIONS OF A PROJECTILE MOTION
For Horizontal direction (x-axis):
Eq. 1: ∆x =
Vx
t
For Vertical direction (y-axis):
Eq. 2:
Vy
=
V0y
+
ay
t
Eq. 3: ∆y = (
Vy+V0y
2
) t
Eq. 4: ∆y =
V0y
t +
1
2
ayt2
Eq. 5:
Vy
2
=
V0y
2
+ 2
ay
∆y
REMEMBER: Be careful with the horizontal (x) and vertical (y) variables. If you have carefully
identified them through honestly understanding the problem, your solutions and answers will be
all right.
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