The equation of motion of a projectile is y=12x−34x2.  The horizontal component of velocity is 3 ms-1. What is the range of the projectile?

Given y=12x−34x2,ux=3ms−1 vy=dydt=12dxdt−32xdxdt At x=0,vy=uy=12dxdt=12ux=12×3=36ms−1ay=ddtdydt=12d2xdt2−32dxdt2+xd2xdt2 But, d2xdt2=ax=0. Hence ay=−32dxdt2=−32ux2=−32×(3)2=−272ms−2 Range, R=2uxuyav=2×3×3627/2=16m Alternatively: We have y=12x−34x2. When projectile again  comes to ground, y=0 and x=R.    0=12R−34R2⇒R=16m