MHB Proving Perpendicular Motion of Two Colliding Spheres

AI Thread Summary
The discussion focuses on proving that two colliding spheres were moving perpendicularly before impact, given that one sphere comes to rest after the collision. The coefficient of restitution is defined as 1/k, with k being greater than or equal to 1. The user has calculated k as -1 and established the initial and final velocity vectors for the sphere of mass m. Additionally, the user seeks to demonstrate that the kinetic energy lost by the stationary sphere is k times the kinetic energy gained by the other sphere. The conversation emphasizes the relationship between momentum, energy conservation, and the geometric implications of the collision.
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Two smooth spheres of masses km and m collide obliquely. the sphere of mass m is brought to rest by the impact. the coefficient of restitution for the collision is 1/k (k greater or equal to 1) Prove before the impact the spheres were moving perpendicular to each other.

i have worked out k=-1. I know the sphere of mass m was xi+0j before and 0i+0j after.
 
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i have worked out the first part
the second part of the question is show that as a result of the collision the kinetic energy lost by the sphere of mass m is k times the kinetic energy gained by the sphere of mass km.
the kinetic energy lost by mass m sphere is .5mx^2
kinetic energy gained by mass km sphere is .5(km)(y)^2-.5(km)(a)^2
Any help?
 

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