A 65.0 kg ice skater moving to the right with a velocity of 2.47 m/s throws a 0.18 kg snowball to the right with a velocity of 24.3 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. _________ m/s to the right (b) A second skater initially at rest with a mass of 62.00 kg catches the snowball. What is the velocity of the second skater after catching the snowball in a perfectly inelastic collision? _________ m/s to the right

Use conservation of momentum:

(65+0.18)*2.47 = .18*24.3 + 65*vf

where vf is final speed of the ice skater

b).Again, use conservation of momentum:

0.18*24.3 = (62+0.18)*vf

To solve this problem, we can use the law of conservation of linear momentum. According to this law, the total momentum before an event is equal to the total momentum after the event, as long as no external forces are acting on the system.

(a) To find the velocity of the ice skater after throwing the snowball, we can calculate the initial momentum of the system (ice skater + snowball) and then divide by the total mass.

First, we find the initial momentum of the ice skater:
Momentum of ice skater = Mass of ice skater × Velocity of ice skater
Momentum of ice skater = 65.0 kg × 2.47 m/s

Next, we find the initial momentum of the snowball:
Momentum of snowball = Mass of snowball × Velocity of snowball relative to the ground
Momentum of snowball = 0.18 kg × 24.3 m/s

Since the snowball is thrown to the right, we have to consider the positive direction for both the ice skater and the snowball.

Total initial momentum = Momentum of ice skater + Momentum of snowball

Now, we divide the total initial momentum by the total mass to find the velocity of the ice skater after throwing the snowball:
Velocity of ice skater after throwing snowball = Total initial momentum / Total mass

(b) To solve part (b), we need to calculate the final velocity of the system when the second skater catches the snowball. This is a perfectly inelastic collision, which means the two skaters stick together after the collision.

In this case, we use the conservation of linear momentum again:

Total initial momentum = Total final momentum

The total initial momentum is the sum of the momentum of the ice skater, the momentum of the snowball, and the momentum of the second skater, initially at rest.

Total initial momentum = (Momentum of ice skater + Momentum of snowball + Momentum of second skater) = 0

Since the initial momentum of the second skater is zero (initially at rest), we can calculate the final momentum of the system (two skaters + snowball).

Total final momentum = (Mass of ice skater + Mass of second skater + Mass of snowball) × Final velocity of the system

To find the final velocity of the system:

Total final momentum / Total mass = Final velocity of the system

Now, let's calculate the answers:

(a) Velocity of the ice skater after throwing the snowball:
Momentum of ice skater = 65.0 kg × 2.47 m/s
Momentum of snowball = 0.18 kg × 24.3 m/s
Total initial momentum = Momentum of ice skater + Momentum of snowball
Velocity of ice skater after throwing snowball = Total initial momentum / Total mass

(b) Velocity of the second skater after catching the snowball:
Total initial momentum = 0 (because there are no external forces acting on the system)
Total final momentum = (Mass of ice skater + Mass of second skater + Mass of snowball) × Final velocity of the system
Total final momentum / Total mass = Final velocity of the system