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Projectiles

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Research on projectiles has been a major concern in procedures or applications that involve objects moving in two dimensions. When someone hurls or launches an object, it follows a specific flight path that is subject to the force of gravity. Scientists focus on this factor to develop kinematic principles describing projectile motion. The analysis of projectiles considers that the influence of other forces such as air resistance on the flight path of a projectile as insignificant. In this regard, if other forces apart from gravity have a considerable influence on the motion a launched or fired object, that object does not meet the criteria of a projectile.

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For example, the analysis of the motion of a helium-filled balloon does not employ concepts of projectile motion since drag and buoyant forces have significant impacts on the motion of the balloon with respect to its weight. This explains why attempts to project helium-filled balloons in a certain direction, and over a long range are often futile. On the other hand, analysis of the motion of an airplane relies on kinematic principles relating to projectile motion (Serway & Jewett 2009, p.79). Although drag and buoyant forces are present, their effect is considerably insignificant as compared to the action of the force of gravity.

At the centre of the concepts of projectile motion are Newton’s laws of motion. Using Newton’s first law of motion, scientists can determine the impacts of the forces acting on a project object such as gravity. The analysis of the acceleration and velocity of a moving object incorporates concepts of Newton’s second law of motion, which describes the net force acting on an object as directly proportional to the objects mass and its acceleration (Giordano 2012, p.99). Using Newton’s laws of motion, scientist can have modelled mathematical equations that describe projectile paths of objects, and help in the calculation of the range, time of flight, maximum range and the velocity of projectiles under study. The range of a projectile is dependent of the velocity of the projectile and the angle at which one launches the projectile. In this regard, the calculation of the maximum range of a projectile considers the intended landing position of a projectile. For projectiles meant to land at a height similar to the height of launching, the realization of maximum range requires a take-off at an angle of 45 degrees irrespective of the velocity involved. However, in cases whereby the projectile should land at a height different from the launching height, maximum range requires a take-off angle that is less than 45 degrees. The disparity between the optimal projection angles, 45 degrees, and take-off angle that guarantees maximum range is dependent on the difference between the take-off and landing height. The difference between the two heights determines the tendency of the take-off angle towards the optimal projection angle. The time of flight of a projectile is dependent on two main initial conditions, which are the initial velocity and vertical position of the projectile (McGinnis, 2005, p.71). Scientific experiments show that the time of flight is directly proportional to the vertical position of a projectile and the initial velocity. In this regard, a ball thrown from a high initial height stays longer in the air than a similar ball thrown from a lower height. Furthermore, throwing a ball upwards with a faster initial velocity means that the ball will stay longer in the air in comparison to a situation in which the initial velocity is slower (Benedek et al. 2000, p.18)

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Projectile motion is a common phenomenon observable in fields that involve moving objects such as sports and the military. In sporting activities such as football, the maximization of the time of flight increases chances of scoring. However, in some sports such as volleyball, minimizing the time of flight of provides higher chances of scoring (Grimshaw 2007, p.50). Within the military, gunners need to ensure that cannons and mortars take-off at an angle of 45 degrees so that fired shots can reach farthest targets. Although scientists consider Newton as the main factor in the breakthrough in the analysis of projectile motion, Galileo laid the foundation upon which Newton develop the laws of motion (Breen, 2009, p.48). Galileo had performed extensive research on motion of bodies and developed the concept of inertia.  He had observed that moving objects tended to remain in the state of motion unless there was external force acting on the object, which upon extensive experimentation Galileo concluded to be frictional forces. Galileo asserted that in the absence of friction, a ball would reach similar heights when rolled on opposite planes. In addition, Galileo observed that the final height of an object was independent of the degree of orientation of the plane on which one rolled the ball.

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Concepts of projectile motion provide a framework upon which analysis can describe the motion of objects using vectors. A projectile comprises of vertical and horizontal components of motion. These components act independently and thus provide a comprehensive approach in analyzing the motion of a projectile. The aspect of independence between vertical and horizontal components of motion is evident by the observation that in the parabolic motion of a canon ball, the horizontal velocity of the ball does not change throughout the motion, but remains equal to the horizontal velocity at the initial stage of launching the ball. The computation of the trajectory of an object relies on the concept of super-positioning the horizontal and vertical components. 

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