Question

a puzzle?????.....no!!!!!a problem.......
a massive ball moving with a speed v collides head on with a fine ball having mass very much smaller than the mass of first ball at rest.the collision is elastic and then immediately after the impact the second ball will move with a speed approx equal to???
use formula v2=2m1/m1+m2*ui+2m2/m1+m2*u2

Answer 1

we apply the conservation of linear momentum and also the conservation of kinetic energy principle.  The collision is completely elastic so there is no loss of energy here.

let  m1 > m2.     u1 = v        u2 = 0  and  v1 and v2 are the speeds after collision.
The balls are colliding head on, so the velocities are all along one axis/straight line.

       m1 v + 0 = m1 v1 + m2 v2      --- (1)
      =>  m1 (v - v1) = m2 v2    --- (2)

   1/2 * m1 * v²  + 0 =  1/2 * m1 * v1² + 1/2 * m2 * v2²
     =>  m1 * v² = m1 * v1² + m2 * v2²  -- (3)
     =>  m1 (v² - v1²) = m2 * v2²        --- (4)

Divide (4) by (2):      Let  v ≠ v1
     v + v1 = v2
   substituting this in equation (2), we get:
             m1 (v - v1) = m2 (v + v1)
             v1 = (m1 - m2) v / (m1 +m2)      --- (5)
             v2 = 2 m1 v /(m1 + m2)        -- (6)