JEE Advanced 2020 Full Test 4 Paper 2

Let the bus be at O when it sends a signal that is detected by the detector as of frequency =1500Hz
∴‌‌f′=(‌

v

v−vB‌cos‌θ

)×1000=1500
∴‌‌cos‌θ=‌

√3

2

‌‌⇒‌‌θ=30∘ By the time signal reaches at S the bus reaches at D. Let this time be t0
∴‌‌t0=‌

OS

v

=‌

lcosecθ

v

Now man fires and the bullet reaches C in time t1 (say). In the same time bus moves from D to C
∴‌‌t1=‌

l

u

; where u= speed of bullet
Also, OD+DC=lcotθ
vBt0+vBt1=lcotθ
VB(‌

lcosecθ

v

)+vB(I∕u)=lcotθ
‌

2

3√3

×2+‌

2

3√3

‌

v

u

=√3
∴‌

v

u

=‌

5

2

∴u=‌

2

5

v=‌

2

5

×340=00136.00m∕s