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I am trying to come up with a formula that estimates the speed of a baseball given the total distance you throw the ball. I know the maximum angle to optimize distance in the x direction is 45 degrees. I am looking for something that includes the friction of air to compute this equation as neglecting friction gives much different results. Does anyone know an equation that would do this? Any help would be much appreciated.

Calvin Cacciamani
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  • You need to add deceleration in the direction of the velocity vector, based on the force of friction, roughly a linear function of the velocity. Try this question on ChatGPT:) What is the best estimate for the friction force on baseball? – Moti May 24 '23 at 18:26
  • $F_f = \frac{1}{2} \rho C_d A v^2$ – Moti May 24 '23 at 18:41
  • where:

    F_f is the friction force ρ is the density of the air (1.225 kg/m3) C_d is the drag coefficient (0.5 for a baseball) A is the cross-sectional area of the ball (0.052 m2) v is the velocity of the ball (m/s)

     – Moti May 24 '23 at 18:41
  • $a = -\frac{F_f}{m}$ , - a is the deceleration rate (m/s^2) - F_f is the friction force - m is the mass of the ball (0.145 kg) – Moti May 24 '23 at 18:43
  • @Moti Can you help me out a little more with this equation? What equation exactly would be the speed of the baseball given a distance? I think your equation has velocity in it which is what I am trying to figure out. – Calvin Cacciamani May 25 '23 at 17:24
  • You write the equation of velocity with the deceleration as a function of time and then use integration for distance and equate it to distance. You could also factor in direction. The equation provides you with drag in the direction of the velocity. – Moti May 26 '23 at 18:25

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