$\begin{array}{1 1}350m/s\\450m/s\\250m/s\\150m/s\end{array} $

Answer : 350m/s

Note: Let's assume that all motion is along the x-axis. Let the earth be frame S and a frame attached to the police car be S'.Frame S' moves relative to frame S with $V_x=50m/s$

If we know an object's velocity measured in one reference frame,S,we can transform it into the velocity that would be measured by an experimenter in a different reference frame, $\overrightarrow{v}=\overrightarrow{v'}+\overrightarrow{V}$ or $\overrightarrow{v'}=\overrightarrow{v}-\overrightarrow{V}$

The bullet is the moving object that will be observed from both frames.The gun is in frame S',so the bullet travels in this frame with $v_x'=300m/s$.

We can transform the bullet's velocity into the earth reference frame :$v_x=v_x'+V_x$

$\;\;\;\;=300m/s+50m/s=350m/s$

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