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A particle with mass m is at rest. A second one, identical to the last one hits the first one. Show that in the case of a perfectly elastic collision (Q=0) the directions of the two particles make a right angle.

You can't assume that both final velocities will be equal. Here's what I've got from using: 1. the conservation of linear momentum. 2. The conservation of kinetic energy (Q=0). 3. Scalar product between the initial velocities.

v=u

u

v

cos(α+β)=(u

And hell, I really can't solve this system...

You can't assume that both final velocities will be equal. Here's what I've got from using: 1. the conservation of linear momentum. 2. The conservation of kinetic energy (Q=0). 3. Scalar product between the initial velocities.

v=u

_{1}cosα + u_{2}cosβu

_{1}sinα = u_{2}sinβv

^{2}=u_{1}^{2}+ u_{2}^{2}cos(α+β)=(u

_{1}^{2}cosα cosβ + u_{2}^{2}sinα sinβ) / (u_{1}u_{2})And hell, I really can't solve this system...

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