Answer:
The velocity of skaters after collision is 0.55 m/s and they are moving to the left
Explanation:
Consider m₁ and m₂ are the masses of two skaters and their initial velocity be v₁ and v₂ respectively.
Consider the velocity along right direction as positive while negative for left direction.
According to the problem,
Mass of first skater, m₁ = 66.0 kg
Mass of second skater, m₂ = 75.0 kg
Velocity of first skater, v₁ = + 2.00 m/s
Velocity of second skater, v₂ = -2.80 m/s
Since, the two skaters grab each other after collision. Hence, they are moving with same final velocity v.
Applying conservation of linear momentum,
Momentum before collision = Momentum after collision
m₁v₁ + m₂v₂ = (m₁+m₂)v
Substitute the suitable values in the above equation.
66 x 2 - 75 x 2.8 = (66 + 75 )v
v = -0.55 m/s
The negative sign denotes that both the skaters are moving in the left direction.