A particle of mass `m_1` experienced a perfectly elastic collision with a stationary particle of mass `m_2`. What fraction of the kinetic energy does the striking particle lose, if
(a) it recoils at right angles to its original motion direction,
(b) the collision is a head-on one?

Explanation

To solve the problem, we need to analyze the two scenarios of the elastic collision involving a particle of mass \( m_1 \) colliding with a stationary particle of mass \( m_2 \).

### Part (a): Recoil at Right Angles

1. **Initial Kinetic Energy Calculation**:
The initial kinetic energy \( KE_i \) of the particle \( m_1 \) is given by:
\[
KE_i = \frac{1}{2} m_1 u_1^2
...