A LevelMathsOCRMaths AMechanicsRevision NotesKinematicsProjectilesHorizontal & Vertical Components of Projectiles

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

Dan Finlay

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OCR Maths A: MechanicsAQA Maths: MechanicsEdexcel Maths: Mechanics

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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

    2-6-1-horizontal-_-vertical-components-diagram-1

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 (ax)and a vertical component (ay)

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

    • No forces are acting horizontally

    • Horizontal speed is constant

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

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

  • The acceleration can be written as 2D vector

a space equals space 0 i space minus space g j space equals space stretchy left parenthesis table row 0 row cell negative straight g end cell end table stretchy right parenthesis space m space s to the power of negative 2 end exponent

What is the initial velocity of a projectile?

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

  • 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, ux = U cosθ

    • vertical component, uy = 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-horizontal-_-vertical-components-diagram-2

Worked Example

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

Examiner Tips and Tricks

  • 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.

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Dan Finlay

Author: Dan Finlay

Expertise: Maths Lead

Dan graduated from the University of Oxford with a First class degree in mathematics. As well as teaching maths for over 8 years, Dan has marked a range of exams for Edexcel, tutored students and taught A Level Accounting. Dan has a keen interest in statistics and probability and their real-life applications.

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