Mathematics: Projectile Motion

Introduction

Mathematics is the study of properties, measurements and relationships of sets and quantities using symbols and numbers. Mathematics is a group of related sciences including geometry, algebra and calculus that studies the interrelationships between quantity, number, space and shape by using specialized notation and this has contributed to human development since the birth of civilization. Calculus is a crucial part of mathematics that studies functions and the ways is which they can be manipulated. Mathematics is a a vibrant, large field of depth, for which calculus is only a small section.

Projectile motion is a section of calculus that studies the motion of an object through air as it experiences the force of gravity. In today’s

In the military a good understanding of projectile motion and kinematics is required. For example, since the 1200s cannons and other weapon projectiles such as catapults have used to fire large rocks into walled cities and without a good understanding of projectile motion this could not be achieved.

Rationale

I chose the topic of projectile motion because of my interest in calculus and its application and because it is a fascinating field of mathematics that is all about mapping change. I was amazed by its ability to calculate the speeds of traveling objects to reach a certain distance. I chose this topic as it was an opportunity to study the effects of gravity, and how it profoundly affects the motion of objects projected upward. I chose to study this in accordance with balls being catapulted into the air as this enables me to apply mathematical principles to calculate distance, velocity, acceleration and area.

Aim

To explore projectile motion using mathematical principles such as integration with a number of different

From this we can illustrate two equations demonstrating the changing velocity in the x-direction and the y-direction:

Vx=Vicosθ

Vy=Visinθ - gt

To calculate the distance traveled by the canon ball kinematic equations must be used to integrate velocity which will give us the distance. Therefore, in-order to calculate the distance travelled both equations must be integrated with respect to time:

Sx=x=(Vicosθ)t

Sy=y=(Visinθ)t - 0.5gt^2

With the information given all necessary ball projectile questions can be calculated.

For example

If a ball is projected from a canon at an angle of 70 degrees with an initial velocity of 1000m/s, how far will the canon ball travel

In order to answer this question a number of steps must be followed before reaching the final