Two hockey players of opposite teams, while trying to hit a hockey ball in the ground collide and immediately become entangled. One has a mass of 60 kg and is moving with velocity 5.0 ms–1 while the other has a mass of 55 kg and is moving faster with velocity 6.0 ms–1 towards the first player. In which direction and what velocity will they move after they become entangled ? Assume that the frictional force acting between the feet of the two players and ground is negligible.
Consider the first hockey player be moving from left to right.
Using sign convention the left to right is taken as positive direction and thus right to left is negative direction.
Let 'm' and 'u' represent the mass and initial velocity of the two players, respectively.
Then
Mass of the 1st palyer, m1 = 60 kg
Velocity, u1 = 5 ms-1
Mass of 2nd player, m2 = 55 kg
Velocity, u2 =-6 ms-1.
The total momentum of the two players before the collision,
= 60 kg x (5 ms-1) + 55 kg x (-6 ms-1)
= -30 kg ms-1
If v is the velocity of the two entangled players after the collision then the total momentum is,
= (m1 + m2) x v
= (60 + 55) kg x v ms-1
= 115 x v ms-1
Acc, to the law of conservation of momentum, we have,
115 x v = -30
v = -30/115
= -0.26 ms-1
Thus the two entangled players would move with a velocity 0.26 ms–1 from right to left, that is in the direction the second player was moving before the collision.