Projectile Motion — Derivation Notes
Projectile motion is the motion of an object thrown into the air under gravity only. To
solve projectile problems, we split the motion into two parts:
• Horizontal motion → constant velocity
• Vertical motion → accelerated motion due to gravity
Velocity Components
Suppose a particle is projected with speed u at an angle θ.
Horizontal component:
u■ = u cosθ
Vertical component:
u■ = u sinθ
Horizontal Motion
Since no force acts horizontally:
a■ = 0
Using:
s = ut + ½at²
x = (u cosθ)t
Page 1
Projectile motion is the motion of an object thrown into the air under gravity only. To
solve projectile problems, we split the motion into two parts:
• Horizontal motion → constant velocity
• Vertical motion → accelerated motion due to gravity
Velocity Components
Suppose a particle is projected with speed u at an angle θ.
Horizontal component:
u■ = u cosθ
Vertical component:
u■ = u sinθ
Horizontal Motion
Since no force acts horizontally:
a■ = 0
Using:
s = ut + ½at²
x = (u cosθ)t
Page 1
