The equation of motion of a projectile is y =12x - 3/4x^2.Given that g=10 ms what is the range of the projectile

Given eqn of projectile motion,                              y = 12 x - 3 x24. Comparing this eqn with standard eqn of projectile motion.                       y = x tanθ - g x22 u2 cos2θ.We get            tanθ = 12     and       g2 u2 cos2θ=34     or    u2 cos2θ = 10×42×3. or                       u cosθ = 2 23  .                    tanθ = sinθcosθ = 12       or   u sinθ =u cosθ×12   or    u sinθ = 24 23.Now the range of projectile = u cosθ× 2u sinθ/g   =   2 23 × 2× 24  23 /10  = 64/3=21.33 m

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