The various aspects of projectile motion have been analyzed many times in this journal. As a sample, over the years, authors have investigated particular details of the path of a projectile and different situations for launching projectiles. Others have written about a nifty way to determine the maximum height of a projectile, finding the range of…

A well-known conclusion from elementary ballistic trajectory analysis is that the horizontal range of a projectile is maximized for a launch angle of 45°. The derivation of this result assumes that the launch speed is the same for all possible launch angles, but this neglects the fact that the work done against gravity by the launching mechanism…

This research studied the effectiveness of the simulation-based learning assisted with scaffolding approach to address students' misconceptions (MCs) about projectile motion. The five MCs were related to the direction of the force acting on an object (MC1), the acceleration of an object at the top of the trajectory (MC2), the directions of…

At our university, students in introductory physics classes perform a laboratory exercise to measure the range of a projectile fired at an assigned angle. A set of photogates is used to determine the initial velocity of the projectile (the launch velocity). We noticed a systematic deviation between the experimentally measured range and the range…

Motivated by quaint woodcut depictions often found in many late 16th and 17th century ballistic manuals of cannonballs fired in air, a comparison of their shapes with those calculated for the classic case of a projectile moving in a linear resisting medium is made. In considering the asymmetrical nature of such trajectories, the initial launch…

We present a nontrigonometric graphical method for predicting the trajectory of a projectile when the angle and initial velocity are known. Students enrolled in a general education conceptual physics course typically have weak backgrounds in trigonometry, making inaccessible the standard analytical calculation of projectile range. Furthermore,…

This study aimed at developing a module in physics based on the assessment of the learning progression of students in physics and science teachers' formative assessment practices. The participants in this study were the Grade 11 students and Junior High School science teachers for the data gathering, science teachers for the design and development…

It's both surprising and rewarding when an old, standard problem reveals a subtlety that expands its pedagogic value. I realized recently that the role of gravity in the range equation for a projectile is not so simple as first appears. This realization may be completely obvious to others but was quite new to me.

This paper describes my attempts to look deeper into the so-called "shoot for your grade" labs, started in the '90s, when I began applying my teaching experience in Russia to introductory physics labs at the College of Charleston and other higher education institutions in South Carolina. The term "shoot for your grade" became popular among…

The problem of determining the angle ? at which a point mass launched from ground level with a given speed v[subscript 0] will reach a maximum distance is a standard exercise in mechanics. There are many possible ways of solving this problem, leading to the well-known answer of ? = p/4, producing a maximum range of D[subscript max] = v[superscript…

Fernández-Chapou and colleagues analyzed projectile trajectories and showed an elliptic property hidden in them. For that analysis, they considered projectiles shot from a point with a common value of speed and different angles of projection. Such projectile paths exhibit some interesting characteristics. For example, pairs of projectiles with…

The air drag constant for different nose shapes of projectiles is determined with the help of a simple method combining a projectile launcher, video tracking technique and spreadsheet computer code for simulating the motion. A projectile launcher with low-cost components is developed to study air drag in projectile motion. The launcher is based on…

Discusses solutions to the problem of maximizing the range of a projectile. Presents three references that solve the problem with and without the use of calculus. Offers a fourth solution suitable for introductory physics courses that relies more on trigonometry and the geometry of the problem. (MDH)

Describes the theory and operation of a demonstration which shows the effect of the inclination angle on the range of a projectile. (CP)

When authoring physics problems, professors may develop an intuition for how much information they need to provide such that the problem has a unique answer and is not over constrained. It is an open question as to whether using intuition leads to a sufficiently broad range of problems. In this paper we discuss a systematic way of authoring…