Horizontal & Vertical Components of Projectiles (OCR A Level Maths A): Revision Note

Horizontal & Vertical Components

What is a projectile?

• A projectile is a particle moving freely, under gravity, in a two-dimensional plane

• Examples of projectile motion include

  • Sports such as basketball, javelin, archery, etc

  • Computer games such as Angry Birds

  

Modelling assumptions with projectiles?

• The modelling assumptions with projectiles are

  • No air resistance, no horizontal forces

  • The projectile moves freely under gravity (no other vertical forces)

  • Ignore spin and the rotation of the projectile

  • Motion is symmetrical along the path of a parabola

What is the acceleration of a projectile?

• As it is 2D there will be a horizontal component to acceleration (a_x)and a vertical component (a_y)

• There will be no horizontal acceleration (a_x = 0)

  • No forces are acting horizontally

  • Horizontal speed is constant

• There will be constant vertical acceleration (due to gravity, a_y = ± g)

• a_y may be positive or negative depending on which direction is taken as positive

• The acceleration can be written as 2D vector

What is the initial velocity of a projectile?

• As it is 2D there will be a horizontal component to the initial velocity(u_x) and a vertical component (u_y)

• A projectile is launched with initial speed U m s^-1 at an angle θ to the horizontal

  • If it is projected below the horizontal then θ would be negative

• Its initial velocity, u m s^-1, is a vector with:

  • horizontal component, u_x = U cosθ

  • vertical component, u_y = U sinθ

• The initial velocity can have a positive or negative vertical component as an object can be projected upwards or downwards