A bus B is moving with a velocity vB in the positive x-direction along a road as shown in the figure. A shooter ‘S ’ is at a distance l from the road. He has a detector which can detect signals only of frequency 1500Hz. The bus blows horn of frequency 1000 Hz. When the detector detects a signal the shooter immediately shoots towards the road along SC and the bullet hits the bus. Find the velocity of the bullet if velocity of sound in air is v = 340 m/s and VBV=233

Let the bus be at O when it sends a signal that is detected by the detector as of frequency = 1500 Hz∴ f′=vv−vBcos⁡θ×1000=1500∴ cos⁡θ=32⇒θ=30∘By the time signal reaches at S the bus reaches at D.Let this time be t0∴ t0=OSv=∣cosec⁡θv…………….(1)Now man fires and the bullet reaches C in time t1 (say). In the same time bus moves from D to C∴ t1=1u; where u= speedofbullet Also, OD + DC = lcotθ    vBt0+vBt1=Icot⁡θ    vBIcosec⁡θv+vB(l/u)=Icot⁡θ    233×2+233vu=3∴     vu=52∴     u=25v=25×340=00136.00m/s