Two skaters collide and grab on to each other on frictionless ice. One of them, of mass 70.0 kg, is moving to the right at 2.00 m/s, while the other, of mass 65.0 kg, is moving to the left at 2.50 m/s. What are the magnitude and direction of the velocity of these skaters just after they collide

Using the law of conservation of momentum which States that "the momentum of momentum of the bodies before collision is equal to the sum of the momentum of the bodies after collision. After collision, the bodies will move with a common velocity v.

If Momentum = mass × velocity

For skater of mass 70kg moving with a velocity of 2m/s, its momentum before collision is expressed as;

Momentum = 70kg×2m/s

Momentum = 140kgm/

For skater of mass 65kg moving with a velocity of 2.5m/s, its momentum before collision is expressed as;

Momentum = 65kg×2.5m/s

Momentum = 162.5kgm/s

Momentum of the bodies after collision is expressed as;

Momentum = (70kg+65kg)v where v is their common velocity after collision)

Momentum = 135v

Using the law above;

140+162.5 = 135v

302.5 = 135v

v = 302.5/135

v = 2.25m/s

The magnitude of the velocity of the bodies just after they collide is 2.25m/s.

Since mass of the skater moving to the right is greater than the one moving to the left, after collision, both of the bodies will be directed towards the right(direction of the body with higher mass).