# 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 $$g=10 \text{ m/s}^2$$
×