Projectile
An object that is thrown or projected into the air, subject only to the acceleration of gravity.
Trajectory of a Projectile
A curved path known as a parabola (in the absence of air resistance).
Primary Force on a Projectile
Gravity (its weight), which acts downwards.
Horizontal Motion of a Projectile
Constant velocity, as there are no horizontal forces acting on it (ignoring air resistance).
Vertical Motion of a Projectile
Constant downward acceleration due to gravity (g = 9.81 m s⁻²).
Resolving a Vector
The process of splitting a vector into two perpendicular components.
Horizontal Component of Velocity (vₓ)
For a velocity v at an angle θ to the x-direction, the component is v cos θ.
Vertical Component of Velocity (vᵧ)
For a velocity v at an angle θ to the x-direction, the component is v sin θ.
Vertical Velocity at Maximum Height
Zero. The projectile momentarily stops moving up before it starts to fall back down.
Sign Convention in Projectile Problems
A consistent direction system (e.g., upwards is positive, downwards is negative) is crucial for calculations.
Equation for Vertical Distance (from rest)
s = ½gt², used for objects thrown horizontally.
Relationship between Horizontal and Vertical Motion
They are independent of one another. Gravity only affects the vertical motion.
Range of a Projectile
The total horizontal distance travelled by the projectile.
Initial Vertical Velocity (uᵧ) for Horizontal Projection
Zero.
Equation of Motion for Horizontal Distance
distance = horizontal velocity × time.
