A player pitches a baseball horizontally toward a speed sensing radar gun The baseball weighs 5 1 8 oz and has a circumference of 9 1 8 in If the speed at x 0 is v 0 90 mi hr, estimate the speed as a function of x Assume that the horizontal aerodynamic drag on the baseball is given by D C D (1 2 v ...

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A player pitches a baseball horizontally toward a speed-sensing radar gun. The baseball weighs 5 1/8 oz

Question:

A player pitches a baseball horizontally toward a speed-sensing radar gun. The baseball weighs 5 1/8 oz and has a circumference of 9 1/8 in. If the speed at x = 0 is v₀ = 90 mi / hr, estimate the speed as a function of x. Assume that the horizontal aerodynamic drag on the baseball is given by D = C_D(1/2 ρv²)S, where C_D is the drag coefficient, ρ is the air density, v is the speed, and S is the cross-sectional area of the baseball. Use a value of 0.3 for CD. Neglect the vertical component of the motion but comment on the validity of this assumption. Evaluate your answer for x = 60 ft, which is the approximate distance between a pitcher’s hand and home plate.