How Do You Derive Projectile Motion With Air Drag Equation?
Use Newton’s 2nd law – force is equal to mass times acceleration. Assuming you’re falling straight down in a constant gravity field, the drag force (D) is exactly opposite the gravity force (aka the weight, W). Thus, the total force is F = W – D Weight is simply mass times the acceleration of gravity, m * g, and you already know that the drag force is proportional to velocity squared, so F = m * g – k * v^2 Now, Newton’s second law says that F = m * a, so m * a = m * g – k * v^2 a = g – k/m * v^2 So, that’s the equation for the acceleration. Here’s where things get tough – we need some calculus to get from here to an equation of motion. Of course, we could evaluate it numerically, by taking small time steps and assume things are constant over the time step. Let’s do that first, since it’s simple. You can use Excel. Open a new sheet. Label the first column will be time, the second will be position, then velocity, acceleration, drag force, and total force. Actually, bump those down a few
