Horizontal & Vertical Components

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

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

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

a = 0 i - g j = (\begin{matrix} 0 \\ - g \end{matrix}) m s^{- 2}

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

2.6.1_WE_Horizontal _ Vertical Components_1

A projectile is launched at an angle of 25° to the horizontal with speed 5 m s^-1 .

Find the initial velocity, u m s^-1 , of the projectile.

2-6-1-horizontal-_-vertical-components-example-solution

Sometimes they may give you the initial velocity as a vector already. To find the initial speed you would find the magnitude of the initial velocity and to find the angle of projection you could sketch a diagram and use trigonometry.
The horizontal speed is always constant so there will never be a point during the motion when the speed of the object is zero. Its minimum speed will be at its maximum height when its vertical velocity is instantaneously zero.

Horizontal & Vertical Components (OCR A Level Maths: Mechanics)