question_answer

               Two hockey players of opposite teams, while trying to hit a hockey ball on the ground, collide and immediately get entangled. One has a mass of 60 kg and was moving with a velocity of 5 m/s. The other has a mass of 55 kg and was moving with a velocity of 6 m/s, towards the first player. In which direction and with what velocity will they move after they become entangled? Assume that the frictional force acting between the feet of two players and ground is negligible.

Answer:

                                            Mass of I player,\[{{m}_{1}}=60kg\] Velocity of I player, \[{{u}_{1}}=5m/s\] Mass of II player, \[{{m}_{2}}=55kg\] Velocity of II player, \[{{u}_{2}}=-6\,m/s\] (as direction of motion is opposite) On getting entangled, final mass M = 60 + 55 =115 kg                                         Final velocity, v = ? As no external force is acting on the system, so from conservation of momentum \[{{m}_{1}}{{u}_{1}}+{{m}_{2}}{{u}_{2}}=Mv\]                                   \[\Rightarrow \]\[(60)(5)+(55)(-6)=115\upsilon \] \[\Rightarrow \]\[300-330=115\upsilon \] or\[\upsilon =\frac{-30}{115}=-\frac{6}{23}m/s\]                                               The entangled mass moves at \[\frac{\text{6}}{\text{23}}\text{m/s}\] towards the first player.