Let the bus be at O when it sends a signal that is detected by the detector as of frequency = 1500 Hz
$\begin{array}{l}\therefore {\mathrm{f}}^{\mathrm{\prime }}=\left(\frac{\mathrm{v}}{\mathrm{v}-{\mathrm{v}}_{\mathrm{B}}\cos \mathrm{\theta }}\right)\times 1000=1500\\ \therefore \cos \mathrm{\theta }=\frac{\sqrt{3}}{2}\Rightarrow \mathrm{\theta }={30}^{\circ }\end{array}$
By the time signal reaches at S the bus reaches at D.
Let this time be t₀
$\therefore {\mathrm{t}}_0=\frac{\mathrm{OS}}{\mathrm{v}}=\frac{\mid \mathrm{cosec}\mathrm{\theta }}{\mathrm{v}}$…………….(1)
Now man fires and the bullet reaches C in time t₁ (say). In the same time bus moves from D to C
$\therefore {\mathrm{t}}_1=\frac{1}{\mathrm{u}}; \mathrm{where} \mathrm{u}= \mathrm{speedofbullet}$
Also, OD + DC = lcot$\mathrm{\theta }$
$\begin{array}{l}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}{\mathrm{v}}_{\mathrm{B}}{\mathrm{t}}_0+{\mathrm{v}}_{\mathrm{B}}{\mathrm{t}}_1=\mathrm{Icot}\mathrm{\theta }\\ \hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}{\mathrm{v}}_{\mathrm{B}}\left(\frac{\mathrm{Icosec}\mathrm{\theta }}{\mathrm{v}}\right)+{\mathrm{v}}_{\mathrm{B}}(\mathrm{l}/\mathrm{u})=\mathrm{Icot}\mathrm{\theta }\\ \hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\frac{2}{3\sqrt{3}}\times 2+\frac{2}{3\sqrt{3}}\frac{\mathrm{v}}{\mathrm{u}}=\sqrt{3}\\ \therefore \hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\frac{\mathrm{v}}{\mathrm{u}}=\frac{5}{2}\\ \therefore \hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\mathrm{u}=\frac{2}{5}\mathrm{v}=\frac{2}{5}\times 340=00136.00\mathrm{m}/\mathrm{s}\end{array}$