and velocity components at some time t, we can find these later time t the formulas for constant acceleration. During a time internal, the average x-component of acceleration x-velocity by an amount So the values of the x-velocity and y-velocity at the Vy + !!J.Vy= Vy + ay!!J.t. But over interval we can regard the acceleration as essentially constant. The acceleration compliantly changing as the velocity components change.

In terms of these quantities, D is given by D = CA. 2 (5-19) idea of our numerical calculation. Typical values of C for baseballs, tennis balls, and ge from 0.2 to 1.0. = -mg – Duu, = may S of acceleration including the effects of both gravity and air drag are ax = -(Dlm) vvx, ay = -g – (D/m) (5-18) ” lZt D depends on the density p of air, the silhouette area A of the body (its front), and a dimensionless constant C called the drag coefficient shape of the body. The direction the direction of v, so we can write Div and the components of regular.Īct is opposite in direction to the corresponding component of f = ~h2 + f/. We’ll assume that the air is still, so v is the velocity tile relative to the ground as well as to the air. At the speed of a tossed tennis magnitude f of the air drag force is approximately proportional to the projectile’s speed relative to the air, I= Du’ where v2 = v} + v/. We must air drag force acting on the projectile. The components of the projectile’s acceleration were si ax = 0, ay = -g. The +z-axis is horizontal, and the +y-axis is vertically upward. That’s what this When we omitted air drag, the only force acting on a projectile with weight w = mi. Fortunately, it is fairly easy to make quite cal approximations to these solutions, using a computer.

We’d now like to extend this analysis to a projectile plane. It’s not difficult to include the force of air resistance in the equations but solving them for the position and velocity as functions of time, or the path, can get quite complex.

We considered how a fluid resistance force falling straight down. But in fact air resistance (often called air drag, or sim major effect on the motion of many objects, including tennis balls, bi airplanes. 5-7 PROJECTILE MOTION WITH AIR RESISTANCEĪ Case Study in Computer Analysis In our study of projectile motion, we assumed that air-rises negligibly small.

Projectile motion with air resistance