The equation of motion of a projectile is :  y  = 12x-34x2The horizontal component of velocity is 3 ms-1. Given that g = 10 ms-2, what is the range of the projectile?

y = 12x - 34x2dydt = 12dxdt-32xdxdtAt x = 0, dydt =12dxdt If θ be the angle of projection, thendydtdxdt = 12 = tan θAlso, if u = initial velocity, then u cos θ = 3Hence, tan θ × cos θ = 36 or u sin θ = 36Range R = u2 sin 2θg = 2u2sin θ cos θg              = 2(u sin θ)(u cos θ)10 = 2×36×310 = 21.6 m