Collision of a stationary ball with a moving ball

[hms.tech]

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 ?

 

[voko]

Can you resolve the equations to obtain c and d expressed in terms of n? If yes, what does that mean?

 

[hms.tech]

Can you resolve the equations to obtain c and d expressed in terms of n? If yes, what does that mean?

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 .

 

[voko]

That proves what you are supposed to prove.