The equation of motion of projectile isy=12x−(3/4)x2The horizontal component of velocity is 3 m/s. What is the range of projectile ? (g = 1.0 m / s2)

Given that,  y=12x−(3/4)x2∴     dydt=12dxdt−32xdxdt At  x=0, dydt=12dxdtIf angle of projection be θ, then(dy/dt)(dx/dt)=tan⁡θ=12If u is initial velocity of projection, then ucos⁡θ=3Therefore,  tan⁡θ×(ucos⁡θ)=36or        usin⁡θ=36Now,   R=u2sin⁡2θg=u2×2sin⁡θcos⁡θg=2(usin⁡θ)(ucos⁡θ)g=2×36×310=21⋅6cm