Taking X -axis along horizontal and Y -axis along vertical, with what minimum speed must a particle be projected from the origin so that it is able to pass through a given point ( 30 m , 40 m ) ? Take g = 10 m s - 2

Step-by-step solution

Using equation of trajectory for a projectile motion : y = x tan ⁡ θ - g x 2 2 u 2 1 + tan 2 ⁡ θ For the projectile to pass through (30 m, 40 m) : 40 = 30 tan α - g (30) 2 2u 2 1 + tan 2 α or 900   tan 2   α   -   ( 6 u 2   tan   α )   +   ( 900   +   8 u 2 )   =   0 For real value of α . The discriminant of a quadratic equation b 2 - 4 a c ≥ 0 ( 6 u 2 ) 2   ≥   3600   ( 900   +