A baseball coach uses a radar device to measure the speed of an approaching pitched baseball. This device sends out electromagnetic waves with frequency $f_0$, and then measures the shift in frequency $\Delta f$ of the waves reflected from the moving baseball. If the fractional frequency shift produced by a baseball is $\frac{\Delta f}{f_0}=2.86\times10^{-7}$, what is the baseball's speed? (Hint: Are the waves Doppler-shifted a second time when reflected off the ball?)
I know that because the ball has a non-relativistic velocity, there are certain terms of the Doppler effect equation that can be simplified, such that $\frac{\Delta f_0}{f}=\frac{u}{c}$, but I do not understand the relation that exists with the waves reflected in the ball.
The answer to the problem is $u=\frac{\Delta f_0}{2f}(c)=\frac{2.86\times 10^{-7}}{2}(3\times10^8\,{\rm m})=42.9\,{\rm m}\,{\rm s}^{-1}=154\,{\rm km}\,{\rm h}^{-1}$
Where does the "$2$" in $u=\frac{\Delta f_0}{2f}(c)$ of the answer come from?