Question

For many years, hitters have claimed that some baseball pitchers have the ability to actually throw a rising fastball. Assuming that a top major leaguer pitcher can throw a 95-mph pitch and impart a 1800-rpm spin to the ball, is it possible for the ball to actually rise? Assume the baseball diameter is 2.9 in. and its weight is 5.25 oz.

Answer 1

given,

speed = 95 mph

N = 1800 rpm

diameter = 2.9 in

weight = 5.25 oz

`\omega = (2\pi N)/(60)`

`\omega = (2\pi * 1800)/(60)`

ω = 188.5 rad/s

U = 95 x 1.467 ft/s

U = 139.33 ft/s

calculate the ratio
`(\omega D)/(2U)`

`(\omega D)/(2U)=(188.5* (2.9)/(12))/(2* 139.33)`

ratio = 0.163

coefficient of lift corresponding to 0.163 from the lift and drag coefficient

C_L = 0.04

ρ is the density of air

Lift produce

`L = (1)/(2)\rho U^2AC_L`

`L = (1)/(2)* 0.002389* 133.33^2* (\pi)/(4)* D^2* 0.04`

`L = (1)/(2)* 0.002389* 133.33^2* (\pi)/(4)* ((2.9)/(12))^2* 0.04`

L = 0.04238 lb

weight

`W = 5.25 oz * 0.625 * (lb)/(oz)`

W = 0.32815 lb