Projectile Motion Cheat Sheet
Projectile Motion:
- An object that is launched into the air that is subject to gravity and is described in two
dimensions.
Projectile Cases:
- There are 3 different cases in which a projectile can be described.
 Case 1: Object that is shot outward with only initial horizontal velocity and no
initial vertical velocity which lands below the origin.
 Case 2: Object that is shot upward at some angle above the horizontal and lands
with zero displacement in the vertical direction.
 Case 3: Object that is shot upward or downward at some angle and lands below
or above the origin.
Case 1 Kinematic Equations for Projectile Motion:
1 2
gt
2
v fy  gt
dy 
v fy  2 gdy
2
dx  v x t
v x  vix  CONSTANT
Kinematic Equations for Projectiles Launched at Some Angle:
vix  vi cos 
viy  vi sin 
dx  vix t
v x  vix  CONSTANT
1 2
gt
2
v fy  viy  gt
dy  viy t 
v fy  viy  2 gdy
2
Projectile Motion Cheat Sheet
Methacton High School Physics Department
2
1
Special Case II Equations for Projectile Motion:
y max  
vi sin  2
2g
2v sin 
t (range)   i
g
v sin 
t (max height )   i
g
v sin 2
Range   i
g
2
Key Hints to Solving Projectile Motion Problems:
-
Draw a picture representing the problem.
-
Set up the variables for both x- and y-directions of the projectile and fill in the given
information. The same rules apply as for the kinematic equations. You need to know 3
to solve the problem, 1 you don’t need and the other you are going to solve for.
𝑣𝑖𝑥 =
𝑣𝑖𝑦 =
𝑡=
𝑣𝑓𝑦 =
𝑑𝑥 =
𝑎𝑦 =
𝑡=
𝑑𝑦 =
-
Time “t” is independent of the horizontal and vertical motion. It’s the variable used to
relate both axis together in the problem. For most problems, solve for “t” in one
direction and use it in the other direction to solve the problem. “t” for both directions
will be equal to one another.
-
Velocity in the x-direction or horizontal velocity remains a constant throughout the
motion of the projectile. Therefore the acceleration in the x-direction is zero.
-
Velocity in the y-direction resembles the motion of an object in free fall.
-
When solving case 2 or case 3 projectile motion problems where the initial velocity is
given in the problem, first split the initial velocity into its horizontal and vertical
velocities.
-
Special case II equations for projectile motion are to be used as a last resort for solving
problems in projectile motion when all else fails.
o
ymax – It’s the maximum height a projectile will reach when launched upward
at some angle.
o
t(range) – The time it takes a projectile to reach the range.
o
t(max height) – The time it takes a projectile to reach maximum height.
o
range – The distance a projectile will cover horizontally after the projectile is
launched at some upward angle with zero displacement in the vertical direction.
Projectile Motion Cheat Sheet
Methacton High School Physics Department
2