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Collision of a stationary ball with a moving ball

  1. Aug 29, 2012 #1
    1. The problem statement, all variables and given/known data

    Two identical balls (same mass and material) , of which the first one (named ball "M") moving in the direction = 3i + 4j collides with the second ball (named ball "S") which is stationary. After the impact, the ball "M" moves in the direction= 3i + 16j while ball "S"
    moves in the direction = i.

    Show that this can happen whatever the initial speed of "M" .

    2. Relevant equations

    P(after impact) = P(before impact) (where P denotes the vector quantity momentum)

    law of restitution.
    3. The attempt at a solution

    U shows Initial velocity

    let U(of M) be = n( 3i + 4j ) [where n= any "scalar" ,thus showing initial velocity]
    let U(of S) be = k (oi+0j) = 0

    V shows final velocity

    let V(of M) be = c( 3i + 16j ) [again "c" is a scalar]
    let V(of S) be = d( i ) [because the impulse and force act horizontally]


    The velocity in j direction remains constant, while momentum is conserved in the x direction.

    so i got two equations :
    1) 3n = 3c + d [from conservation of momentum in i direction]
    2) 4n = 16c ⇔ n/c = 4 [velocity remains unchanged in j direction]

    I don't know what to do next, how do i prove this ?
     
  2. jcsd
  3. Aug 29, 2012 #2
    Can you resolve the equations to obtain c and d expressed in terms of n? If yes, what does that mean?
     
  4. Aug 29, 2012 #3
    Certainly,

    c=n/4

    and d= 9n/4

    It means that for any value of "n" there is a value of "c" and "d" .

    I don't see how this helps me .
     
  5. Aug 29, 2012 #4
    That proves what you are supposed to prove.
     
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