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" .
P(after impact) = P(before impact) (where P denotes the vector quantity momentum)
law of restitution.
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 ?