Formula: Head-on Central Collision

$$v'_2 ~=~ v_1 \, \left( \frac{2m_1}{ m_1 + m_2 } \right) ~+~ v_2 \, \left( \frac{m_2 - m_1}{ m_1 + m_2 } \right)$$ $$v'_2 ~=~ v_1 \, \left( \frac{2m_1}{ m_1 + m_2 } \right) ~+~ v_2 \, \left( \frac{m_2 - m_1}{ m_1 + m_2 } \right)$$

Velocity of the second body (after)

$$ v'_2 $$ Unit $$ \frac{\mathrm m}{\mathrm s} $$

Velocity of the second body after the head-on elastic collision.

This formula describes a collision between two bodies. Elastic means that the conservation of energy is fulfilled. For example, the body should not deform or rotate after the collision.

If you want to calculate the velocity $v'_1$ of the first body after the collision, use this formula: \[ v'_1 ~=~ v_1 \, \left( \frac{m_1 - m_2}{ m_1 + m_2 } \right) ~+~ v_2 \, \left( \frac{2m_2}{ m_1 + m_2 } \right) \]

Velocity of the first body (before)

$$ v_1 $$ Unit $$ \frac{\mathrm m}{\mathrm s} $$

Velocity of the first body before the collision.

Velocity of the second body (before)

$$ v_2 $$ Unit $$ \frac{\mathrm m}{\mathrm s} $$

Velocity of the second body before the collision.

Mass of the first body

$$ m_1 $$ Unit $$ \mathrm{kg} $$

Mass of the first body. This formula assumes that the mass has not changed after the collision.

Mass of the second body

$$ m_2 $$ Unit $$ \mathrm{kg} $$

Mass of the second body. This formula assumes that the mass has not changed after the collision.