Discussion Forum

A particle  of mass m moving in the x-direction which speed 2v is hit by another particle of mass 2m moving in the y-direction with speed v. If the collision is perfectly inelastic, the percentage loss in the energy during the collision is close to 

Answer:

Explanation:

Central idea.    concept of relative motion can be applied to predict the nature of motion of one particle with respect to the other.

   Consider ,the stones thrown up simulaneously  as shown in the diagram below.

   Considering motion of the second particle with respect to the first we have realtive acceleration

       $|a_{21}|=|a_{2}-a_{1}|=g-g=0$

Thus, motion of first particle is straight line with respect to second particle till the first particle strikes ground at a time given by

                 $-240=10t-\frac{1}{2}\times 10\times t^{2}$

   or             $t^{2}-2t-48=0$

  or              $t^{2}-8t+6t-48=0$

   or    t=8,-6  (not possible)

Thus, distance  covered by second particle  with respect to first particle in 8 s is

    $s_{12}=(v_{21})t=(40-10)(8s)$

      $=30\times 8=240m$

  Similarly, time taken by second particle to strike the ground is given by

  $-240=40t-\frac{1}{2}\times10\times t^{2}$

 or           $-240=40t-5 t^{2}$

or         $5 t^{2}-40t-240=0$  

 or    $ t^{2}-8t-48=0$

    $ t^{2}-12t+4t-48=0$

  or  t (t-12)+4(t-12)=0

   or t=12,-4             (not possible)

Thus, after 8 s, magnitude of relative velocity will increase up to 12 s when second particle strikes the ground.