Time of Flight, Maximum Height & Range question from MHT CET 2023 (13 May, Shift 1)

Answer: (b)

1. Farthest a bullet can land is the maximum range at $45^\circ$: $R_{max} = \frac{u^2}{g}$.
2. Bullets fired in all directions cover a circle of radius $R_{max}$.
3. $A = \pi R_{max}^2 = \frac{\pi u^4}{g^2}$
4. So the answer is (b) $\frac{\pi u^4}{g^2}$.