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Aoife O'Malley 11131519

Stephanie Steiger 10099468

Cannon Trajectory

Proposed Solution

Key Information

What Factors were considered??

Extensions

Visual Representation

Who would this project be suitable for?

Visual Representation Continued

Mathematical concepts required

To successfully complete this project a comprehensive understanding of the following mathematical concepts are necessary;

Visual Representation Continued

Don't take our word for it...Try it yourself :)

Maximum Point is exactly half way along the Horizontal Disposition

Assumptions

Due to the cannon being released inside, there is no air resistance on the object.

Projectile is Influenced by the Force of Gravity at

32.2 ft/sec

Quadratic function is formulated by the projectile, using both Horizontal and Vertical calculations

Strengths and Weaknesses of the Model

Possible Extensions

In the 17th century, the mathematician Galileo suggested that the magnitude of air resistance for a moving body, is proportional to the speed of the object. This was a huge improvement on the work of his student, Tartaglia, who formulated the Law of falling bodies, which neglected the incorporation of air resistance.

Also within this century, the book entitled Opera Geometrica published by Torricelli, clarified and extended Galileo’s work on ballistics; it included new constructions, new methods, and new expressions. The publication of this book, provided people with the understanding of geometry in order to advance their use of weaponry, etc.

History of Mathematics

The renowned physicist Aristotle identified the presence of two types of motion:

- Natural motion - this is the resistance of a medium such as air or water upon an object in which it falls e.g. falling stone.

- Violent motion - this is when a force is applied to a given object through the aid of the medium e.g. pushing an object.

Strengths:

- It develops students metacognitive skills.

- It encourages students to utilise a vast range of mathematical concepts.

- It's extension is easily adaptable to a classroom setting.

- It incorporates a number of cross-curricular links including physics.

Weaknesses:

- Idenfying the key assumptions of this task may prove to be difficult to the student.

- Students may find it difficult to start the proposed solution without a knowledge of physics.

References

Ashby, R. (2013) Cloning Bullets In Scratch [online], available; [accessed 21 Apr 2017].

Cannon image, available on; https://www.google.ie/search?q=canon&source=lnms&tbm=isch&sa=X&ved=0ahUKEwiLjNv9rrPTAhVBBMAKHXtoANsQ_AUIBigB&biw=1366&bih=643#tbm=isch&q=cannon&imgrc=NZU9Fe6jum5dTM:&spf=387.

Einstein, A., 1906. The principle of conservation of motion of the center of gravity and the inertia of energy. Ann. Phys, 20, pp.627-633.

Halloun, I.A. and Hestenes, D., 1985. Common sense concepts about motion. American journal of physics, 53(11), pp.1056-1065.

Horizontal And Vertical Displacement [online] (2017) [online], Physicsclassroom.com.

JP, K. (2010) How To Make A Slingshot With A Ballon And Toilet Paper Roll [online], available; [accessed 20 Apr 2017].

Statement of Task

A cannon is any piece of artillery that uses gunpowder, or some other explosive-based propellants, to launch a projectile across a distance. In the 17th century cannons typically had a muzzle velocity of about 460 feet per second.

Based on this information, explore the optimum barrel elevation angle on a cannon if you are trying to maximise the distance that your projectile travels?

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