Drag force equation, projectile

[Mag|cK]

Hello everyone. I have researched from the internet that the drag force equation for projectile motion is either F= C p a v^2 or F= 0.5 C p a v^2. Which one is the correct one? The initial speed I am dealing with is about 20m/s. And what's the value for C for a normal tennis ball. Other sites give too big of a range value for C.

Secondly, for calculations, for the vertical component, I need to divide the drag force calculation into 1.when the ball goes up and 2. when the ball goes down. Because in #1, gravity has negative value, and in #2, gravity has positive value. Right? Yet, why many sites i have seen including the posted PDF files on the internet about projectile motion calculation with air resistance just simply generalize the vertical component calculation into 1 equation?

Lastly, about the equation
a(acceleration vertical component)= -1/m (Fdrag sinX + mg)

when the ball travels downward, isn't angle X negative, hence giving the value sinX negative, and consequently positive drag force?

And do you have any suggestions for good 'projectile with air resistance' sites?

Thank you very much.

 

[rcgldr]

Gravity would always be a downwards (negative vertical) force. The only force that varies is drag. The difference between the .5 x Cd and the 1.0 x C equations is C has incorporated the .5, while Cd is the coefficient of drag. Cd for a tennis ball will vary based on the fuzz and the spin.

 

[Mag|cK]

"Secondly, for calculations, for the vertical component, I need to divide the drag force calculation into 1.when the ball goes up and 2. when the ball goes down. Because in #1, gravity has negative value, and in #2, gravity has positive value in the equation. Right? Yet, why many sites i have seen including the posted PDF files on the internet about projectile motion calculation with air resistance just simply generalize the vertical component calculation into 1 equation?"

Anyone has any answers on this one?