3.1.3 Projectile motion

How far projectiles can travel depends on several factors. It is important to realise that the vertical and horizontal motions of the ball are independent of each other. Assuming no air resistance:

• the vertical velocity changes due to acceleration of free fall
• the vertical displacement and time of flight can be calculated using the equations of motion
• horizontal velocity remains constant

The horizontal velocity of the projectile is constant because acceleration and velocity are vectors. The acceleration of free fall is vertically downwards and the component of this acceleration in the horizontal direction is zero. This is because horizontal acceleration = g cos 90° = 0.

The path of the projectile is curved because the vertical component of its velocity increases with time whilst the horizontal component is unaffected. The magnitude of the actual velocity (v) of the projectile can be calculated from he vertical and horizontal components of the velocity (vx and vy):

v = √((vx)² + (vy)²)

The angle made by the velocity to the horizontal is given by:

θ = tan^-1 ((vy)/(vx))

When a projectile is fired upwards the motion can still be analysed in terms of the independent motion in the horizontal and vertical directions. The horizontal component of the velocity if vcosθ and the initial vertical component of the velocity if vsinθ.