A sphere of mass 0.3 kg moving with a velocity of $\text{4}\text{m/s}$ collides with another sphere of mass 0.5 kg which is at rest. Assuming the collision to be elastic, their velocities after the impact are

${\text{u}}_{\text{1}}=4\text{m/s,}{\text{u}}_{\text{2}}=0\text{m/s}$                                                                  

${\text{v}}_2=\frac{\left({\text{m}}_2-{\text{m}}_1\right){\text{u}}_2}{\left({\text{m}}_{\text{1}}+{\text{m}}_{\text{2}}\right)}+\frac{2{\text{m}}_{\text{1}}{\text{u}}_1}{\left({\text{m}}_{\text{1}}+{\text{m}}_{\text{2}}\right)}$

$=\frac{\left(-0.3+0.5\right)\left(0\right)}{\left(0.3+0.5\right)}+\frac{2\left(0.3\right)\left(4\right)}{\left({\text{m}}_{\text{1}}+{\text{m}}_{\text{2}}\right)}$

$=0+\frac{2\times 0.3\times 4}{0.8}$

${\text{v}}_{\text{2}}=3\text{m/s}$

${\text{v}}_1=\frac{\left({\text{m}}_{\text{1}}-{\text{m}}_{\text{2}}\right){\text{u}}_{\text{1}}}{\left({\text{m}}_{\text{1}}+{\text{m}}_{\text{2}}\right)}+\frac{2{\text{m}}_{\text{2}}{\text{u}}_{\text{2}}}{\left({\text{m}}_{\text{1}}+{\text{m}}_{\text{2}}\right)}$

$=\frac{\left(0.3-0.5\right)4}{\left(0.3+0.5\right)}+\frac{2\left(0.5\right)\left(0\right)}{\left(0.3+0.5\right)}$

$=\frac{-0.2\times 4}{0.8}+0$

${\text{v}}_1=-1\text{m/s}$