If the equation of motion of a projectile is given by y=12 x- 3 4 x^2 and its horizontal component of velocity is 3 ~ms ⁻¹ , then find its range. (g=10 ~ms ⁻² )

Step-by-step solution

Let u and be the velocity of projection and angle of projection, respectively. Given that, horizontal component of velocity, u_x=u =3 ~m / s Equation of projectile motion is given by y=12 x- 3 4 x^2 ...(i) We know, General equation of projectile motion, y=x - g x^2 2 u^2 ^2 ...(ii) Comparing Eqs. (i) and (ii), we get =12 =12 =12 Multiplying on both side by (u)u =12(u )=12 3 i.e. u =36 ~m / s Now, using the expression of range, aligned & R= u^2 2 g & R= 2 u^2 g aligned R= 2(u )(u ) g [Using identity 2 =2 ] Substitut