# Drag force equation, projectile

1. May 18, 2007

### 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?

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.

2. May 19, 2007

### 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.

3. May 19, 2007

### 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?