Projectile Motion
First: Projectile motion is the movement of an object in an arc under the influence of gravity alone.
Important Note: The key to solving projectile motion problems is separating the horizontal motion from the
vertical motion. Never attempt to solve a projectile motion problem before separating it into horizontal and
vertical motion.
Time (𝜟𝒕) is shared
Horizontal motion (motion at constant speed) Vertical motion (free fall)
Acting force: None Acting force: Gravitational force (𝐹𝑔 )
Acceleration: None Acceleration: Acceleration due to gravity )𝑔 ≈ 10𝑚/𝑠 2 (
Velocity (𝑣𝑥 ): Constant Velocity (𝑣𝑦 ): Variable
𝛥𝑥 𝑣𝑓𝑦 = 𝑣𝑖𝑦 + 𝑔𝛥𝑡
𝑣𝑥 =
𝛥𝑡
2 2
𝑣𝑓𝑦 = 𝑣𝑖𝑦 + 2𝑔𝛥𝑦
1
𝛥𝑦 = 𝑣𝑖𝑦 𝛥𝑡 + 𝑔𝛥𝑡 2
2
Notes:
① ● If the question concerns horizontal motion, we use the equation for constant velocity.
● If the question concerns vertical motion, we use the equations for free fall.
● If the question relates to both motions (i.e., time), then the calculation depends on the given
information.
② Horizontal velocity (𝑣𝑥 ) is constant → 𝑣𝑖𝑥 = 𝑣𝑓𝑥
③ At maximum height (𝛥𝑦𝑚𝑎𝑥 ) → 𝑣𝑦 = 0
ѵy = 0
ѵᵢy = ѵᵢ sinѲ ѵᵢ
yₘₐₓ Fg
(Maximum height)
Ѳ
ѵᵢₓ = ѵᵢ cosѲ
xₘₐₓ
(Horizontal range)
First: Projectile motion is the movement of an object in an arc under the influence of gravity alone.
Important Note: The key to solving projectile motion problems is separating the horizontal motion from the
vertical motion. Never attempt to solve a projectile motion problem before separating it into horizontal and
vertical motion.
Time (𝜟𝒕) is shared
Horizontal motion (motion at constant speed) Vertical motion (free fall)
Acting force: None Acting force: Gravitational force (𝐹𝑔 )
Acceleration: None Acceleration: Acceleration due to gravity )𝑔 ≈ 10𝑚/𝑠 2 (
Velocity (𝑣𝑥 ): Constant Velocity (𝑣𝑦 ): Variable
𝛥𝑥 𝑣𝑓𝑦 = 𝑣𝑖𝑦 + 𝑔𝛥𝑡
𝑣𝑥 =
𝛥𝑡
2 2
𝑣𝑓𝑦 = 𝑣𝑖𝑦 + 2𝑔𝛥𝑦
1
𝛥𝑦 = 𝑣𝑖𝑦 𝛥𝑡 + 𝑔𝛥𝑡 2
2
Notes:
① ● If the question concerns horizontal motion, we use the equation for constant velocity.
● If the question concerns vertical motion, we use the equations for free fall.
● If the question relates to both motions (i.e., time), then the calculation depends on the given
information.
② Horizontal velocity (𝑣𝑥 ) is constant → 𝑣𝑖𝑥 = 𝑣𝑓𝑥
③ At maximum height (𝛥𝑦𝑚𝑎𝑥 ) → 𝑣𝑦 = 0
ѵy = 0
ѵᵢy = ѵᵢ sinѲ ѵᵢ
yₘₐₓ Fg
(Maximum height)
Ѳ
ѵᵢₓ = ѵᵢ cosѲ
xₘₐₓ
(Horizontal range)
