At major league baseball games it is commonplace to flash on the scoreboard a sp

Question

At major league baseball games it is commonplace to flash on the scoreboard a speed for each pitch. This speed is determined with a radar gun aimed by an operator positioned behind home plate. The gun uses the Doppler shift of microwaves reflected from the baseball, as we will study in a later chapter. The gun determines the speed at some particular point on the baseball's path, depending on when the operator pulls the trigger. Because the ball is subject to a drag force due to air, it slows as it travels 18.44 m toward the plate. Use the equation below to find how much its speed decreases.

Suppose the ball, with a mass of 0.145 kg and cross-sectional area of 4.20 10-3 m2, leaves the pitcher's hand at 91.0 mi/h = 40.7 m/s. Ignoring its vertical motion, determine the speed of the pitch when it crosses the plate. (Assume a drag coefficient, D, of 0.305 and a resistive force, R, of 1.2 N.)

Explanation / Answer

so the drag coefficient,D=0.305, ,

cross-sec area,A=4.20x10-3,

mass of the ball, m=0.145kg

k=(0.305)(4.20x10-3) / 0.145

k=8.834x10-3

V=V0e-kx

V=(43.8m/s)e(-8.834x10-3)(18.44m)

V=37.2155

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