Final answer:
In an elastic collision between a moving particle X of mass m and a stationary particle Y of mass 3m, the speed of both particles after the collision is 2sqrt(5) m/s, which correlates with answer option D.
Step-by-step explanation:
The question involves a head-on elastic collision between two particles, one of which is stationary. When an elastic collision occurs, two key principles apply: conservation of momentum and conservation of kinetic energy. For particle X with mass m moving at a speed of 5.0 m/s and colliding with stationary particle Y with mass 3m, we use these principles to find the speeds after the collision.
By conservation of momentum, the total momentum before the collision equals the total momentum after the collision: m*5.0 + 3m*0 = m*Vx + 3m*Vy, where Vx and Vy are the final velocities of particles X and Y respectively.
By conservation of kinetic energy, the total kinetic energy before collision equals the total kinetic energy after collision: 0.5*m*5.02 = 0.5*m*Vx2 + 0.5*3m*Vy2.
After solving these equations, we find that the speed of particle X after the collision is 2sqrt(5) m/s and the speed of particle Y is 2sqrt(5) m/s. Therefore, the correct answer is D. 2sqrt(5) m/s, 2sqrt(5) m/s.