Question

It has been found that two hockey players of opposite teams, when tried to hit a hockey ball on the ground, collided and immediately became entangled. One is having a mass mentioned as $60kg$ and was in a motion with a velocity $5$. At the same time, the other one was having a mass $55kg$ and was moving with a greater velocity of $6$ towards the first player. What will be the direction and the velocity of both the persons even after they become entangled? Let us suppose that the frictional force acting between the first two players and ground is negligible.

Answer 1

The total momentum will be a constant. First of all find the total momentum of the two players by taking the sum of the product of the mass of the person and the velocity of the same person and the product of mass of the other one and his velocity. Then find the momentum after the collision. From this calculate the final velocity.

Complete answer:
The total momentum of the players can be found by the equation given as,
$P={{m}_{1}}{{u}_{1}}+{{m}_{2}}{{u}_{2}}$
Where ${{m}_{1}}$ be the mass of the first player which has been mentioned as $60kg$.
${{u}_{1}}$ be the velocity of the first player mentioned as,
${{u}_{1}}=5$
${{m}_{2}}$ be the mass of the second player which has been mentioned as,
${{m}_{2}}=55kg$
And ${{u}_{2}}$ be the velocity of the second player given as,
${{u}_{2}}=6$
Substituting the values in the equation will give,
$\begin{aligned} & P=60\times 5+55\times 6 \\\ & \Rightarrow P=300-330 \\\ & \Rightarrow P=-30kgm{{s}^{-1}} \\\ \end{aligned}$
The total momentum of two after the collision will be found by the equation,
$P=\left( {{m}_{1}}+{{m}_{2}} \right)V$
Substituting the values in the equation will give,
$\begin{aligned} & -30=\left( 60+55 \right)V \\\ & \therefore V=\dfrac{-30}{115}=-0.26m{{s}^{-1}} \\\ \end{aligned}$
Therefore the final velocity has been obtained.

Note:
The momentum conservation says that the amount of the momentum will remain fixed. That is the momentum will be neither destroyed nor be created. The momentum can be changed through the action of forces as defined as Newton's laws of motion.