Let u and θ be the velocity of projection and angle of projection, respechively. Given that, horizontal component of velocity. ux=u‌cos‌θ=3m∕s Equation of projectile motion is given by y=12x−
3
4
x2 ...(i) We know, General equation of projectile motion, y=x‌tan‌θ−
gx2
2u2cos2θ
...(ii) Comparing Eqs. (i) and (ii), we get tanθ = 12 ⇒
sin‌θ
cos‌θ
=12 sin‌θ=12‌cos‌θ Multiplying on both side by (u) u‌sin‌θ=12(u‌cos‌θ)=12×3 i.e. u‌sin‌θ=36m∕s Now, using the expression of range. R=
u2‌sin‌2‌θ
g
R=
2u2‌sin‌θ‌cos‌θ
g
R=
2(u‌sin‌θ)(u‌cos‌θ)
g
[Using identity sin‌2‌θ=2‌sin‌θ‌cos‌θ ] Substituting the values, we get R=