A proton undergoes a head on elastic collision with a particle of unknown mass Initially at rest and rebounds with 16/25 of its initial kinetic energy. Calculate the ratio of the mass of the unknown particle with respect to the mass of the proton.

In an elastic collision, both momentum and kinetic energy are conserved. We are given that a proton undergoes a head-on elastic collision with a particle of unknown mass initially at rest, and after the collision, the proton rebounds with 16/25 of its initial kinetic energy.

Let the mass of the proton be mpm_p, the mass of the unknown particle be mxm_x, and the initial velocity of the proton be upu_p. Initially, the unknown particle is at rest, so its initial velocity is ux=0u_x = 0.

Conservation of Momentum:

The total momentum before and after the collision must be equal. Let the final velocities of the proton and the unknown particle after the collision be vpv_p and vxv_x, _____ __________ ________ ____ ____ _______ ___ ___ ___ ___.
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