A particle \(A\) of mass \(m_A\) is projected vertically upwards with velocity \(100 \text{ m/s}\). In its return journey it collides with another particle \(B\) of mass \(m_B\), \(320 \text{ m}\) below the maximum height attained by particle \(A\). Particle \(B\) has a horizontal velocity \(200 \text{ m/s}\) and vertical velocity \(0 \text{ m/s}\). Find the distance between the places they hit the ground.

**Details and assumptions**

- \(2m_A=m_B\)
- The collision has a coefficient of restitution \(e=\frac{1}{2}\)
- Acceleration due to gravity \(g=10 \text{ m/s}^2\)

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