Oblique Collision Between Two Spheres : Incomplete info?

[evansmiley]

Two smooth spheres of masses 4 kg and 2 kg impinge obliquely.
The 2 kg mass is brought to rest by the impact.
(i) Prove that, before impact, they were moving in directions perpendicular to each other.
(ii) Show that, as a result of impact, the kinetic energy gained by the 4 kg mass is equal to half that lost by the 2 kg mass.

I'm having trouble proving the first part because to prove it i'd need to show that e = 1/2 however no value of e is given. Is this possible to solve or is the information incomplete?

 

[jbsteele]

(i) Without knowing the coefficient of restitution (e) between the two spheres, we cannot prove that they were moving in directions perpendicular to each other before impact. (ii) Assuming that the coefficient of restitution is 1/2, then the kinetic energy gained by the 4 kg mass is equal to half that lost by the 2 kg mass. This can be shown using the law of conservation of momentum and the equation for coefficient of restitution: Let v1 and v2 be the velocities of the 4 kg and 2 kg masses respectively before the impact. After the impact, the velocity of the 4 kg mass is v1' and the velocity of the 2 kg mass is 0. Using the law of conservation of momentum, we get: m1*v1 + m2*v2 = m1*v1'm1*v1 - m1*v1' = m2*v2m2*v2 = m1*(v1 - v1')v2 = m1/m2 * (v1 - v1')Using the equation for coefficient of restitution, we get: v1' = -e*v2Substituting this into the above equation, we get: v2 = m1/m2 * (v1 + e*v2)v2 = m1/m2 * v1 * (1 + e)Rearranging this equation and solving for v2, we get: v2 = (m1/m2) * (v1 / (1+e))For our case where e = 1/2, we get: v2 = (m1/m2) * (v1 / (1+1/2))v2 = (m1/m2) * (v1 / (3/2))v2 = (2/3) * v1Therefore, the kinetic energy lost by the 2 kg mass is: KE2 = (1/2) * m2 * v2^2 = (1/2) * 2kg * ((2/3) * v1)^2 = (4/9) * m1