A 74.5 kg ice skater moving to the right with a velocity of 2.62 m/s throws a 0.21 kg snowball to the right with a velocity of 23.8 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.
1 m/s to the right
(b) A second skater initially at rest with a mass of 63.00 kg catches the snowball. What is the velocity of the second skater after catching the snowball in a perfectly inelastic collision?
2 m/s to the right

(a) Using a coordinate system fixed to the ground, apply momentum conservation as follows:

(74.5+0.21)*2.62 = V'*74.5 + 0.21*23.8

V' is the skater's final velocity.
195.74 = 74.5 V' + 4.998

V' = 2.56 m/s
(positive is to the right)

(b) Apply momentum conservation again
0.21*23.8 = (63.00 + 0.21) V
Solve for V

(a) Well, it seems like the ice skater is pretty skilled at throwing snowballs. After throwing the snowball, the skater's velocity would still be 2.62 m/s to the right. So, the ice skater continues on their merry way at 2.62 m/s to the right!

(b) Ah, the poor second skater who was just minding their own business. In a perfectly inelastic collision, the two skaters would stick together like glue. So, after catching the snowball, the second skater would be pulled to the right with a velocity of 2 m/s. Guess they couldn't escape the snowball's impact after all!

To solve this problem, we can use the principle of conservation of momentum. The momentum before the snowball is thrown is equal to the momentum after it is thrown.

(a) Let's calculate the initial momentum of the ice skater before throwing the snowball:
initial momentum of ice skater = mass of ice skater * velocity of ice skater

Before throwing the snowball:
mass of ice skater = 74.5 kg
velocity of ice skater = 2.62 m/s

initial momentum of ice skater = 74.5 kg * 2.62 m/s = 194.99 kg·m/s to the right

Now, let's calculate the momentum of the snowball:
momentum of snowball = mass of snowball * velocity of snowball

mass of snowball = 0.21 kg
velocity of snowball = 23.8 m/s

momentum of snowball = 0.21 kg * 23.8 m/s = 4.998 kg·m/s to the right

The total momentum after throwing the snowball should be equal to the initial momentum (conservation of momentum):
total momentum after = initial momentum of ice skater + momentum of snowball

total momentum after = 194.99 kg·m/s to the right + 4.998 kg·m/s to the right
total momentum after = 199.988 kg·m/s to the right

Now, let's calculate the velocity of the ice skater after throwing the snowball:
velocity of ice skater after throwing snowball = total momentum after / mass of ice skater

mass of ice skater = 74.5 kg
total momentum after = 199.988 kg·m/s

velocity of ice skater after throwing snowball = 199.988 kg·m/s / 74.5 kg ≈ 2.68 m/s to the right

So, the velocity of the ice skater after throwing the snowball is approximately 2.68 m/s to the right.

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

The total momentum before the collision is equal to the momentum after the collision.

Before the collision:
momentum of ice skater = mass of ice skater * initial velocity of ice skater
momentum of snowball = mass of snowball * velocity of snowball
momentum of second skater = mass of second skater * initial velocity of second skater

mass of ice skater = 74.5 kg (as given earlier)
initial velocity of ice skater = 2.62 m/s (as given earlier)
mass of snowball = 0.21 kg (as given earlier)
velocity of snowball = 23.8 m/s (as given earlier)
mass of second skater = 63 kg
initial velocity of second skater = 0 m/s (initially at rest)

(total momentum) before = (momentum of ice skater) + (momentum of snowball) + (momentum of second skater)

(total momentum) before = (74.5 kg * 2.62 m/s) + (0.21 kg * 23.8 m/s) + (63 kg * 0 m/s)

(total momentum) before = 194.99 kg·m/s + 4.998 kg·m/s + 0 kg·m/s
(total momentum) before = 199.988 kg·m/s to the right

Since it is a perfectly inelastic collision, the two skaters stick together after the collision. Therefore, the mass of the combined skaters is the sum of their individual masses.

(combined mass) = mass of ice skater + mass of second skater

(combined mass) = 74.5 kg + 63 kg
(combined mass) = 137.5 kg

Now, let's calculate the velocity of the combined skaters after the collision:
velocity of combined skaters after collision = total momentum before / combined mass

velocity of combined skaters after collision = 199.988 kg·m/s / 137.5 kg
velocity of combined skaters after collision ≈ 1.454 m/s to the right

Therefore, the velocity of the second skater after catching the snowball in a perfectly inelastic collision is approximately 1.454 m/s to the right.

To solve this problem, we can use the principle of conservation of momentum. The principle states that the total momentum before an event is equal to the total momentum after the event, in the absence of external forces.

(a) The total momentum before the snowball is thrown is the sum of the momentum of the ice skater and the momentum of the snowball:
initial momentum = (mass of ice skater × velocity of ice skater) + (mass of snowball × velocity of snowball)

Let's calculate the initial momentum:
initial momentum = (74.5 kg × 2.62 m/s) + (0.21 kg × 23.8 m/s)
initial momentum = 194.69 kg·m/s + 5.018 kg·m/s
initial momentum = 199.71 kg·m/s

To find the velocity of the ice skater after throwing the snowball, we'll use the conservation of momentum principle. The total momentum after the event is equal to the initial momentum:
total momentum after = (mass of ice skater + mass of snowball) × velocity of ice skater after

Let's solve for the velocity of the ice skater after throwing the snowball:
199.71 kg·m/s = (74.5 kg + 0.21 kg) × velocity of ice skater after
199.71 kg·m/s = 74.71 kg × velocity of ice skater after

Dividing both sides by 74.71 kg gives:
velocity of ice skater after = 199.71 kg·m/s / 74.71 kg
velocity of ice skater after = 2.67 m/s

Therefore, the velocity of the ice skater after throwing the snowball is approximately 2.67 m/s to the right.

(b) In a perfectly inelastic collision, the two objects stick together and move as one. The total momentum after the collision is the sum of the initial momenta of the two objects.

Let's calculate the initial momentum of the second skater and the snowball:
initial momentum = (mass of second skater × velocity of second skater) + (mass of snowball × velocity of snowball)

Since the second skater is initially at rest, the initial velocity of the second skater is 0:
initial momentum = (63.00 kg × 0) + (0.21 kg × 23.8 m/s)
initial momentum = 0 + 5.018 kg·m/s
initial momentum = 5.018 kg·m/s

To find the velocity of the second skater after catching the snowball, we'll use the conservation of momentum principle. The total momentum after the collision is equal to the initial momentum:
total momentum after = (mass of second skater + mass of snowball) × velocity of second skater after

Let's solve for the velocity of the second skater after catching the snowball:
5.018 kg·m/s = (63.00 kg + 0.21 kg) × velocity of second skater after
5.018 kg·m/s = 63.21 kg × velocity of second skater after

Dividing both sides by 63.21 kg gives:
velocity of second skater after = 5.018 kg·m/s / 63.21 kg
velocity of second skater after ≈ 0.08 m/s

Therefore, the velocity of the second skater after catching the snowball in a perfectly inelastic collision is approximately 0.08 m/s to the right.