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Introduction
We show how one can solve most if not all, introductory-level projectile motion problems in one or maybe two lines. To this end, we forgo convention. We demote clock time ##t## to a parameter of secondary importance and ditch the independence of motion in the vertical and horizontal directions.
Starting from the first principles, we develop two primary equations that relate five “basic” parameters to each other: ##\Delta x##, ##\Delta y##, ##v_{0x}##, ##v_{0y}## and ##v_y## (standard definitions). We view the solution of projectile motion problems as equivalent to solving a system of five equations with the five basic parameters as the five unknowns. Once the system is solved, the time of flight, if one must have it, is just the ratio ##\Delta x/v_{0x}##.
To sharpen the implementation of the primary equations, we recombine them to derive three auxiliary shortcut equations that facilitate the identification of equation parameters with given variables. Finally, we...
Projectile motion is the motion of an object through the air or space under the influence of gravity, with no other forces acting on it.
To solve projectile motion problems in one or two lines, you can use the equations of motion: x = x0 + v0t + 1/2at^2 and v = v0 + at, where x is the final position, x0 is the initial position, v0 is the initial velocity, a is the acceleration, and t is the time.
The key factors to consider when solving projectile motion problems are the initial velocity, angle of launch, and acceleration due to gravity.
Yes, the same equations can be used to solve projectile motion problems in both one and two dimensions. However, in two dimensions, you will need to break down the motion into horizontal and vertical components.
Some common mistakes to avoid when solving projectile motion problems are forgetting to account for the acceleration due to gravity, using the wrong units, and not considering the direction of the velocity and acceleration vectors.