Answer to Question #320578 in Mechanics | Relativity for Priscy

Question

A ball of mass 5.0kg moving with a velocity of 10meter per second collides with a 15.0kg ball moving with a velocity of 4 meterper second. If both balls stick together after collision. Calculate their common velocities after impact if they initially move in

a. same direction

b. Opposite direction

Answer 1

The law of conservation of momentum says

$$m_1\vec v_1+m_2\vec v_2=m_1\vec v_1'+m_2\vec v_2'$$

(a)

$$m_1v_1+m_2 v_2=(m_1+m_2)v'$$

$$v'=\frac{m_1v_1+m_2 v_2}{m_1+m_2}=\frac{5.0*10+15*4}{5.0+15}=5.5\:\rm m/s$$

(b)

$$m_1v_1-m_2 v_2=(m_1+m_2)v'$$

$$v'=\frac{m_1v_1-m_2 v_2}{m_1+m_2}=\frac{5.0*10-15*4}{5.0+15}=-0.5\:\rm m/s$$