Two skaters collide and grab on to each other on frictionless ice. One of them, of mass 66.0 kg , is moving to the right at 2.00 m/s , while the other, of mass 75.0 kg , is moving to the left at 2.80 m/s. What are the magnitude and direction of the velocity of these skaters just after they collide?

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.