In the elastic collision of heavy vehicle moving with a...

In the elastic collision of heavy vehicle moving with a velocity $10 \mathrm{~ms}^{-1}$ and a small stone at rest, the stone will fly away with a velocity equal to
(a) $40 \mathrm{~ms}^{-1}$
(b) $20 \mathrm{~ms}^{-1}$
(c) $10 \mathrm{~ms}^{-1}$
(d) $5 \mathrm{~ms}^{-1}$

Key Concepts

Conservation of Kinetic Energy

For elastic collisions, the total kinetic energy of the system is conserved along with momentum. This conservation law provides a second independent equation that, together with the momentum conservation equation, enables the complete determination of the final velocities in the collision scenario.

Mass Ratio Approximation

When one body is much more massive than the other, the more massive body's velocity remains almost unchanged, and the smaller body can gain a significantly larger velocity. This approximation helps simplify the calculations in collisions by assuming that the heavy object's state does not greatly change, allowing easier determination of the small object's rebound speed.

Elastic Collision

An elastic collision is one in which both momentum and kinetic energy are conserved. This concept is crucial for analyzing collisions where none of the kinetic energy is lost to deformation, heat, or sound. It forms the basis for deriving the velocities of colliding bodies after collision using conservation laws.

Conservation of Momentum

In any collision, the total momentum of the system before the impact must equal the total momentum after the impact, provided no external forces act on the system. This principle is used to set up equations that relate the velocities and masses of the bodies involved, allowing the determination of unknown quantities post-collision.

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