• two putty balls of equal masses moving in mutually perpendicular directions with equal speed ,stick together after the collision .if the balls were intially moving with a velocity of 45underroot 2 m/s each feind the velocity of the combined mass after the collision

Dear Student,

          Let the mass of each ball be 'm' and they are moving with same velocity, v = 452  m/s. After collision they got combined , the mass of combined system= 2m,  let the system moves with velocity v'.
  Now from figure below,
applying conservation law of momentum, in x-axis,
                                                       mv + 0 = 2mv'cosθ​       ...........(i)
       Now in y - axis, 
                                                      mv + 0  = 2mv' sin θ     ...........(ii)

Now adding (i) and (ii) we get,
                                                        2mv = 2mv'(cosθ​ +sinθ)
                                                  v' = v(cosθ+sinθ)From figure, θ=45o v' =  v(cos45o+sin45o) = v12+12 v'  = 452×22 =45 m/sso the velocity of combined system, v' = 45 m/s.


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