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## Homework Statement

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" .

## Homework Equations

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 ?