In The Art of War Sun Tzu says that ¨victorious warriors win first and then go to war while defeated warriors go to war first and then seek to win¨.
Students preparing for their IGCSE and A level exams this year need to be confident that they will win first by preparing themselves assiduously throughout the year and not just seek to win by attending to their preparation during the final weeks before the examinations..
Physics has always been at the heart of war; from the development of new materials and weapons to understanding and predicting the trajectories of ballistics for both good but also for evil, reflective of who we are as a people, physics and the knowledge that comes with it has been and is now at the heart of the world we live in.
It was with war in mind that the study of kinematics (or the analysis of motion) probably came into being. Up until the development of the SUVAT equations there was no way of predicting accurately the motion of a projectile. With these powerful equations we could identify the position of a cannon ball, arrow or bullet as it sped through space and time.
What makes the SUVAT equations different from the Euclidean mathematics which had reigned for the previous two millenia is that it introduced into that frozen mathematical world the notion of time (T). The fourth dimension.
The SUVAT equations were developed throughout the ages by countless thinkers whose names are now forgotten but who each added their grain of sand nonetheless to the partially built cathedral that is human understanding. Galileo was amongst the first to observe that the path of a projectile (arrow, bullet etc) through space and time is in the form of a parabola. Always in the form of a parabola.To analyse this motion it needs to be broken down into its component parts. A tennis ball on its journey through the air really experiences two simultaneous journeys and you will need to be able to identify both of these journeys simultaneously. When dealing with projectile problems you will need to break down the motion into horizontal and vertical components.
In any given problem there is always the potential for any given value of SUVAT to have two values, one a horizontal value and the other a vertical. With one exception. What always links both horizontal and vertical motion when you freeze the projectiles´ motion ?
If the motion is frozen as in an exam question the variable linking both… is time. Remember that the projectile will reach the end of its journey, both horizontal journey and vertical journey at the same time. Everything else about its horizontal and vertical journeys will probably be different but journeys end will occur at the same time.
What is the difference between horizontal and vertical motion ? As far as A-level is concerned; with horizontal motion acceleration is zero (friction and air resistance usually ignored) and with vertical motion it will be that of the free fall caused by gravity usually given as 9.81 ms^2.
So how to go about solving IGCSE and A level problems ?
Break the motion down into two components. Make a SUVAT for both the horizontal and vertical motion and write down the value for each.
Remember that the horizontal component of motion will undergo no acceleration and so the velocity (V) is constant ie it remains the same as U. For horizontal motion u=s/t as there is no acceleration or s=ut+½ at^2 . Since a=0 s=ut 🙂
That leaves vertical motion which IS subject to a the constant downward force of gravity producing an acceleration of 9.81 m/s^2. So now we know that our final velocity (v) will not equal our initial velocity (u) as our projectile has travelled through space and time. You can not travel through space without time 🙂 Time stretches everything out. Or everything would happen at once. No future episodes, or past.
I am running out of time and space for this post so will end it here with a final quote from Sun Tzu (read the book:) ¨to be successful you must believe in yourself¨ !!