A 68.0 kg ice skater moving to the right with a velocity of 2.55 m/s throws a 0.16 kg snowball to the right with a velocity of 27.5 m/s relative to the ground.

(a) What is the velocity of the ice skater after throwing the snowball? Disregard the friction between the skates and the ice.

(b) A second skater initially at rest with a mass of 60.50 kg catches the snowball. What is the velocity of the second skater after catching the snowball in a perfectly inelastic collision?

To find the solution, we can use the law of conservation of momentum, which states that the total momentum before an event is equal to the total momentum after the event, assuming no external forces act on the system.

Let's break down the problem step-by-step:

(a) To find the velocity of the ice skater after throwing the snowball, we need to consider the momentum of both the ice skater and the snowball before and after the throwing motion.

The momentum (p) of an object is given by the formula:
p = mass * velocity

For the ice skater initially:
Mass of the ice skater (m1) = 68.0 kg
Velocity of the ice skater (v1) = 2.55 m/s

The momentum of the ice skater before the throwing motion is:
p1 = m1 * v1

Now, let's consider the snowball:
Mass of the snowball (m2) = 0.16 kg
Velocity of the snowball (v2) = 27.5 m/s

The momentum of the snowball before the throwing motion is:
p2 = m2 * v2

Since there are no external forces acting on the ice skater and the snowball during this interaction, the total momentum before the throwing motion is equal to the total momentum after the throwing motion:

Total initial momentum = Total final momentum
(p1 + p2)initial = (p1 + p2)final

Since the ice skater and the snowball are moving in the same direction, we can write:
p1initial + p2initial = p1final + p2final

Substituting the respective values, we get:
(m1 * v1)initial + (m2 * v2)initial = (m1 * v1)final + (m2 * v2)final

Solving this equation will give us the velocity of the ice skater after throwing the snowball.

(b) To find the velocity of the second skater after catching the snowball in a perfectly inelastic collision, we need to again use the law of conservation of momentum.

In an inelastic collision, the objects stick together after the collision, and their combined mass moves with a common final velocity.

Let's consider the second skater:
Mass of the second skater (m3) = 60.50 kg

Assuming the velocity of the second skater after catching the snowball is v3, we can write the equation using the conservation of momentum:

Total initial momentum = Total final momentum
(m1 * v1)initial + (m2 * v2)initial = (m1 + m2 + m3)final * vf

Substituting the values, we get:
(m1 * v1)initial + (m2 * v2)initial = (m1 + m2 + m3)final * vf

Solve this equation to find the velocity of the second skater after catching the snowball.

It is important to note that these calculations ignore the friction between the skates and the ice, as stated in the given question.