Moving directly at one another, two hydrogen-like atoms collide head-on with each other. After this collision occurs, both of the atoms will cease their motion entirely. Each atom will then emit a photon with a wavelength of 102.6 nm which corresponds to a 3 -> 1 transition. Determine what the initial speed of each atom was before they collided with each other?

During an experiment, a physicist uses a firecracker to break apart a cube. The cube is placed on a rough horizontal floor. When the explosion happens, the cube is broken into two pieces which move in opposite directions. The first piece of mass M₁ moves on the floor 65 cm before coming to rest while the second piece of mass M₂ moves a distance d. Find the distance d if M₁ = 5 M₂. Consider that the coefficient of kinetic friction for both pieces is the same.

Proton radioactivity is an unusual type of radioactive decay that occurs when a proton is ejected from a nucleus. During a nuclear experiment, proton (mass 1 u) emission was observed from the decay of ⁵³₂₇Co (mass 53 u). The proton's speed in the laboratory frame was measured to be 1.42 × 10⁷ m/s. Find the recoil speed of the daughter nucleus ⁵²₂₆Fe.

Two carts, A, with mass m and B, with mass 2m, are placed on a frictionless horizontal track. They are connected by a massless spring with a spring constant k, which is initially compressed by an amount X from its natural length. The system is released from rest with the spring in its compressed state. Find the speeds of carts A and B when they no longer are in contact with the spring.

Inside a particle accelerator, a charged particle moves at a speed of 410. m/s. After some time, the particle disintegrates and emits a lighter particle of mass 2.00 u that moves in the same direction as the direction of motion of the initial particle. As a result, the disintegrated heavy particle gets slowed down to 380. m/s. If the mass of the initial particle is 238 u, calculate the velocity with which the lighter particle moves after being emitted.

A subatomic particle of mass 2M collided elastically with another subatomic particle of mass 4M. The initial speed of the former particle was V, while the latter was stationary. Given that after the collision, the former particle was scattered at 90°, calculate the final speeds of the particles.

A ball of mass 3M moves with a velocity of V toward another stationary ball of mass 6M. Eventually, it collides elastically with the stationary ball and scatters at an angle of 90° with its initial direction of motion. The ball of mass 6M scatters at an angle of 30° with the direction of motion of 3M. Calculate the fraction of the initial kinetic energy of the ball of mass 3M that is transferred to the other ball after the collision. (Assume that there is no friction.)