Solving Projectile Motion Using the Quadratic Formula

Miacademy & MiaPrep Learning Channel

This educational video bridges the gap between abstract mathematics and physical reality by demonstrating how parabolas and the quadratic equation are used to solve projectile motion problems in physics. The narrator begins by addressing the common student question, "When will I ever use this?" by explaining the historical context of parabolas, noting how Ancient Greek geometry was later applied by Galileo to describe the motion of objects moving through the air. The video visualizes how the trajectory of a projectile, like a cannonball, maps perfectly onto an inverted parabola. The core of the video is a step-by-step tutorial on applying the quadratic formula to a specific physics problem involving a rock ejected from a volcano. The video breaks down the problem-solving process: identifying known variables, decomposing velocity vectors using trigonometry, setting up the kinematic equation, and rearranging it into the standard quadratic form ($ax^2+bx+c=0$). It explicitly connects the mathematical coefficients $a$, $b$, and $c$ to physical quantities like gravity, initial velocity, and displacement. This resource is highly valuable for bridging Algebra II and High School Physics curricula. It provides a concrete application for the quadratic formula, moving beyond rote memorization to practical implementation. Teachers can use this video to introduce 2D kinematics, review the quadratic formula in a new context, or facilitate a cross-curricular lesson connecting math and science standards. The inclusion of a mnemonic song for the formula adds a memorable engagement element for students.