Question

A 10 kg ball and 20 kg ball approach each other with velocities 20 m/s and 10m/s. What are their velocities after collision of it is perfectly elastic??

Answer 1

since their momentum are equal, they will cancel out and eventually the velocity will be 0 m/s.

Answer 2

Let the masses of two bodies are denoted as $m_{1}\ and\ m_{2}\ respectively$

As per the question $m_{1} =\ 10\ kg$

                                 $m_{2} =\ 20\ kg$

Let the initial velocities of the bodies are denoted as  $u_{1}\ and\ u_{2}\ respectively$

Here $u_{1} =\ 20\ m/s$

         $u_{2} =10\ m/s$

As per the question, the collision is perfectly elastic. We are asked to calculate the final velocities of the two bodies.

Let the final velocities are denoted as  $v_{1}\ and\ v_{2}\ respectively$

As the collision is elastic in nature ,

$v_{1} =\frac{m_{1}- m_{2}} { m_{1} +m_{12}}* u_{1} +2\frac{m_{2}} {m_{1} +m_{1}}*u_{2}$

      $= \frac{10-20}{10+20}*20+2 \frac{20}{10+20} *10$

      $=-\frac{20}{3} +\frac{40}{3}\ m/s$

      $=\frac{20}{3}\ m/s$

      $=6.67\ m/s$

similarly we can calculate the velocity of 20 kg ball.

$v_{2} =\frac{m_{2}- m_{1}} { m_{1}+ m_{2}}* u_{2} +2\frac{m_{1}} { m_{1} +m_{2}}* u_{1}$

     $=\frac{20-10}{20+10} *10+2\frac{10}{10+20} *20\ m/s$

     $=\frac{10}{30} *10+2*\frac{10}{30} *20$

     $=\frac{10}{3} +\frac{40}{3}$

     $=\frac{50}{3}\ m/s$

     $=\ 16.67\ m/s$    [ans]