Calculating Tennis Ball Trajectory: Force and Integration Explained

[diegorodriguez]

1. How to get x,y positions for a tennis ball at each time t given total force exerted?2. We consider Drag force D, Lift Force L and Gravitation force W

D=1/2*(0.55+1/((22.5+4.2*(v/(w*R))^2.5)^0.4))*pi*R^2*d*v^2
L=1/2*(1/(2+(v/(w*R))))*pi*R^2*d*v^2
W=m*g
​

as described in
http://www.physics.usyd.edu.au/~cross/TRAJECTORIES/42. Ball Trajectories.pdf

where v, speed; w, angular speed;R, radius;d, density;m, mass

3. I suppose we need to integrate force twice on time t for Fx and Fy given a Serve Angle Ro and Serve Speed vi, but how?

 

[haruspex]

As far as I am aware, there is no analytic solution for 2D motion with drag.