(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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.

V=V_{0}e^{-kx}

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 98.0 mi/h = 43.8 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.)

3. The attempt at a solution

How do i know what thekstands for inV=V?_{0}e^{-kx}

so i assume it is the drag coefficient, D, of 0.305

43.8e^{(-0.305x18.44)}= 0.158m/s

the answer looks very wrong, and it is wrong indeed.

but how do i know what is the k in the equation stands for? or perhaps i shouldn't just sub in the value like that?

may i know what is the proper way of doing this kind of question?

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# Resistive force of air

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