Two hockey players collide at center ice.
Player 1 m = 70 kg Vi= 10 m/s7.
Player 2 m = 90 kg Vi= - 3 m/s + 4 m/s
If the two players become tangled up and travel together, what is their final velocity?
Good
To find the final velocity of the two players when they become tangled up and travel together, we can apply the principle of conservation of momentum.
The principle of conservation of momentum states that the total momentum of an isolated system remains constant before and after an interaction. In this case, the two hockey players collide and form an isolated system, as no external forces are acting on them.
The momentum of an object is given by the product of its mass and velocity. Therefore, the momentum of player 1 (p1) before the collision is given by p1 = m1 * V1, where m1 is the mass of player 1 and V1 is their initial velocity. Similarly, the momentum of player 2 (p2) before the collision is given by p2 = m2 * V2, where m2 is the mass of player 2 and V2 is their initial velocity.
Before the collision:
p1 = m1 * V1 = 70 kg * 10 m/s = 700 kg·m/s
p2 = m2 * V2 = 90 kg * (-3 m/s) = -270 kg·m/s
Since player 2 has an initial velocity in the negative direction, we assign a negative sign to the momentum.
The total momentum of the system before the collision is the sum of the individual momenta:
ptotal = p1 + p2 = 700 kg·m/s + (-270 kg·m/s) = 430 kg·m/s
After the collision, the two players become tangled up and travel together, so they have the same final velocity (Vf). We can calculate their final velocity using the total momentum of the system (ptotal) and the combined mass of the players (m1 + m2).
Using the principle of conservation of momentum, we have:
ptotal = (m1 + m2) * Vf
Vf = ptotal / (m1 + m2)
Substituting the values:
Vf = 430 kg·m/s / (70 kg + 90 kg)
Vf = 430 kg·m/s / 160 kg
Vf ≈ 2.688 m/s
Therefore, the final velocity of the two players when they become tangled up and travel together is approximately 2.688 m/s.