Crazy Projectiles

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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