Question

a 2.2kg ball moves to the right with a speed of 6.5m/s and collided with a 1.8kg ball moving at 1.8m/s in the opposite direction. if this is a completely elastic collision determine the velocity of each balll

Answer 1

$m_1v_1+m_2v_2=mv_1'+m_2v_2'$ and $\frac{m_1v^2_1}{2}+\frac{m_2v^2_2}{2}=\frac{m_1v'^2_1}{2}+\frac{m_2v'^2_2}{2}$

$2.2\cdot 6.5-1.8\cdot1.8=2.2v_1'+1.8v_2'\to 11.06=2.2v_1'+1.8v_2'$

$2.2\cdot 6.5^2+1.8\cdot 1.8^2=2.2v'^2_1+1.8v'^2_2 \to 98.782=2.2v'^2_1+1.8v'^2_2$

$v_1'=\frac{11.06-1.8v_2'}{2.2}$

$2.2\cdot (\frac{11.06-1.8v_2'}{2.2})^2+1.8v'^2_2=98.782$ $\to$

$v_2'=7.33m/s$

$v_1'=\frac{11.06-1.8v_2'}{2.2}=\frac{11.06-1.8\cdot 7.33}{2.2}=-0,97m/s$

Answer

$v_1'=-0,97m/s$

$v_2'=7.33m/s$