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 + 8 u 2 ) or ( u 4 - 800 u 2 ) ≥ 9 , 00 , 00 or ( u 2 - 400 ) 2 ≥ ( 2 , 50 , 000 ) or u 2 - 400 ≥ 500 or u 2 ≥ 900 or u ≥ 30 m s - 1