The correct option is D 200√5 m/s
Formula for range is,
R=u2sin2θg
Let the muzzle velocity be u.
For maximum range, numerator should be maximized.
Since speed for fired shell is equal to u m/s every time. (u constant)
Maximum range will correspond to maximum value of sin2θ, which is 1.
sin2θ=1⇒2θ=90∘
Thus, θ=45∘ should be the angle of firing (angle of projection) for shell to obtain maximum range.
Rmax=u2g
⇒20×103=u210
∴u=√20×104=200√5 m/s