Oblique Impact of Smooth Spheres

[SpartaGhost]

Hey, I'm struggling with this question, any help would be great.

A sphere of mass m impinges obliquely on a sphere of mass M, which is at rest. The coefficient of restitution between the spheres is e. Show that if m=eM, the directions of motion after impact are at right angles

My attempt was:

mUcosα = mV1 + MV2 (1)
V2-V1 = e(Ucosα) (2)

since m=eM
=> eMcosα = eMV1 + Mv2 then /m

so subtracting the equations gives
eUcosα = eV1 + V2
- eUcosα = V2 - V1

=> 0 = eV1 + V1
e = -1

which is where I just don't understand what to do now :(

 

[HallsofIvy]

Well, if you want to show that " the directions of motion after impact are at right angles" you had better work with the directions of motion hadn't you? Yet, I see no indication of x or y components. You see to be treating V1 and V2 as numbers- that is, assuming the two masses move in a straight line.

 

[SpartaGhost]

Hi, I used the parallel and perpendicular components and yeah the masses move in a linear direction.