Two skaters collide and grab on to each other on frictionless ice. One of them, of mass 79.0 kg , is moving to the right at 4.00 m/s, while the other, of mass 61.0 kg , is moving to the left at 2.50 m/s.

A- What are the magnitude of the velocity of these skaters just after they collide?
B- What are the direction of the velocity of these skaters just after they collide?
a-to the left
b-to the right

(a) the magnitude of the velocity of these skaters just after they collide is 1.169 m/s

(b) the direction of the velocity is to the right

Explanation:

Given;

mass of the first skater, m₁ = 79.0 kg

mass of the second skater, m₂ = 61.0 kg

initial velocity of the first skater, u₁ = 4.00 m/s

initial velocity of the second skater, u₂ = 2.50 m/s

From the principle of conservation of linear momentum, total momentum before collision must be equal to total momentum after collision.

since the two skaters collide and grab on to each other, it is inelastic collision.

we assume momentum towards right positive and momentum towards left negative.

m₁u₁ - m₂u₂ = v(m₁ + m₂)

where;

v is the magnitude of the velocity after collision for inelastic collision.

(79 x 4) - (61 x 2.5) = v(79 + 61)

163.5 = 140v

v = 163.5/140

v = 1.169 m/s

Since this common velocity is positive, then the direction is towards right.