Topic Nine (1.9): Projectiles

Introduction

Time for the fun stuff! Cannon balls, bullets and throwing balls. This topic explains how to solve the motion of projectiles (thrown objects, flying freely under gravity). This is simply an application of the suvat equations, but separately in horizontal and vertical planes.

By resolving into vertical and horizontal components we can solve these separately, then re-combine at any point, using Pythagoras and the tangent ratio to give magnitude and direction of velocity. If air resistance is low, the horizontal velocity is constant and the vertical motion follows a quadratic equation, so the projectile path will be a parabola. We can use our knowledge of this quadratic function to easily predict the properties of the path.

The classic example of this is a bullet fired from a gun. The interesting fact is that if you drop a bullet at the same time that one is fired from a gun, they both hit the ground at the same time. You can calculate this using $LaTeX: s=\frac{1}{2}{gt}^2$ $s=\frac{1}{2}{gt}^2$ , and calculate the horizontal distance travelled by the bullet as it hits the ground using $LaTeX: s=\frac{u+v}{2}t$ $s=\frac{u+v}{2}t$ .

You can actually take this a step further and work out the velocity of the bullet as it hits the ground. Work out the bullet’s final vertical velocity and final horizontal velocity, then combine these velocities as you would for two forces at right angles.

Reading

Edexcel International AS/A Level Physics Student Book 1 pages 28 to 33

Tasks

Complete the following:

Read pages 28 to 29 of the textbook.

WATCH – Projectile Motion and ‘Suvat’ (YouTube: ScienceShorts) Links to an external site.

WATCH – ‘Projectile Angle Cliff’ (YouTube: PGHS Physics) Links to an external site.

WATCH – Motion Equations Example 2 (YouTube: Talkboard) Links to an external site.

WATCH – What is Gravity? (YouTube) Links to an external site.

SIMULATION – Projectile Motion (Walter Fendt) Links to an external site. Start by clicking the button to show velocity.

COMPLETE – Gameboard: ‘Trajectories’ (Isaac Physics) Links to an external site.

COMPLETE – Gameboard: ‘Equations of Motion in 2D’ (Isaac Physics) Links to an external site.

READ and COMPLETE questions using simulator – Projectile Simulator. Launch Interactive and Complete Activities 1, 2 and 3 (Physics Classroom) Links to an external site.

Complete the questions on page 29. You will find the answers in General Resources under the heading Textbook Answers. Download Textbook Answers.

Top Tips

Make sure that you understand the following key points:

Visualise clearly: Make a sketch!
Calculate the motion in horizontal and vertical planes separately.
Use suvat equations.
You can combine your two planes at the end of your calculations to work out the resultant velocity.
Projectiles follow parabola paths; peak height occurs where vertical velocity is zero.
Even if a projectile goes up then down again, we can solve in ONE step by picking a positive direction and sticking to it. Take care to choose the ‘suvat’ equation that uses just the four quantities you are interested in.
To find magnitude and direction at any point use Pythagoras and the Tangent ratio with the and
To find distance to landing point, solve vertically for time at landing, then use constant horizontal velocity for horizontal distance.
Remember you can use the quadratic equation if using $LaTeX: s=ut+\frac{1}{2}at^2$ $s=ut+\frac{1}{2}at^2$ , if time is required.
Assume no air resistance and horizontal component for velocity is always constant, with zero acceleration.

Key Terms

Add the following key terms with definitions to your word list:

Horizontal plane
Vertical plane
Projectile
Parabola

Consolidate

Now consolidate your understanding by working through these additional resources:

Read the ‘Thinking Bigger’ section on page 30.
Complete the questions in the two boxes on page 31.

REVIEW Revision Notes – Physics Factsheet: ‘Combined Notes – Unit 1 Edexcel Physics A-level’, ‘1.3 Mechanics’ (Physics and Maths Tutor) Links to an external site.

Complete the exam practice questions on pages 32 to 33. You will find the answers in General Resources under the heading Textbook Answers. Download Textbook Answers.

Quiz

Complete Quiz 01: Motion. If you score less than 90%, try again.

Assignment

When you have completed all the activities and are fully prepared and feel confident with the material, you should complete Assignment One and submit it to your tutor via Canvas for marking and feedback.