A point particle with mass m and velocity v_0 undergoes a collision with a stationary particle of the same mass. Following the impact, the total kinetic energy of the system is observed to be 50% greater than the initial kinetic energy. Determine the magnitude of the relative velocity between the two particles after the collision.

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EEJ MAIN Physics QUESTION #7027

Question 1

A point particle with mass $m$ and velocity $v_0$ undergoes a collision with a stationary particle of the same mass. Following the impact, the total kinetic energy of the system is observed to be $50\%$ greater than the initial kinetic energy. Determine the magnitude of the relative velocity between the two particles after the collision.

$\frac{v_{0}}{2}$
$\frac{v_{0}}{\sqrt{2}}$
$\frac{v_{0}}{4}$
$\sqrt{2}v_{0}$✔️

Correct Answer Explanation

Initial $KE = \frac{1}{2}mv_0^2$. Final $KE = 1.5 \times (\frac{1}{2}mv_0^2)$. Let final velocities be $v_1$ and $v_2$. By conservation of momentum, $mv_0 = m(v_1 + v_2)$, so $v_0 = v_1 + v_2$. The relative velocity is $|v_2 - v_1|$. Using the relation $2(v_1^2 + v_2^2) = (v_1 + v_2)^2 + (v_1 - v_2)^2$ and substituting energy and momentum values, we find the relative velocity is $\sqrt{2}v_0$.

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