A(n) 86.6 kg person throws a(n) 0.06 kg snow- ball forward with a ground speed of 42.3 m/s. A second person, of mass 41.5 kg, catches the snowball. Both people are on skates. The first person is initially moving forward with a speed of 2.06 m/s, and the second person is initially at rest.

What is the velocity of the first person im- mediately after the snowball is thrown? Dis- regard friction between the skates and the ice.
Answer in units of m/s

The 2nd person does not matter for this problem. To conserve momentum before and after the throw,

(86.6)(2.06) + 0(0.06) = (86.6)(v) + (42.3)(0.06)

thank you!

To find the velocity of the first person immediately after the snowball is thrown, we can use the principle of conservation of momentum.

The momentum of an object is given by the product of its mass and velocity. According to the conservation of momentum, the total momentum before the snowball is thrown should be equal to the total momentum after the snowball is thrown, assuming no external forces act on the system.

Initially, the first person has a mass of 86.6 kg and a velocity of 2.06 m/s, and the second person has a mass of 41.5 kg and is at rest. The snowball has a mass of 0.06 kg and a ground speed of 42.3 m/s.

The total momentum before the snowball is thrown is the sum of the momenta of the two people, which can be calculated as:
Momentum_before = (mass_1 * velocity_1) + (mass_2 * velocity_2)
= (86.6 kg * 2.06 m/s) + (41.5 kg * 0 m/s)
= 178.596 kg m/s

The total momentum after the snowball is thrown is the sum of the momenta of the two people and the snowball. Let the velocity of the first person after throwing the snowball be v.

Momentum_after = (mass_1 * velocity_1') + (mass_2 * velocity_2') + (mass_snowball * velocity_snowball)
= (86.6 kg * v) + (41.5 kg * 0 m/s) + (0.06 kg * 42.3 m/s)

Since momentum is conserved, we can set the total momentum before equal to the total momentum after and solve for v:
Momentum_before = Momentum_after

178.596 kg m/s = (86.6 kg * v) + (0.06 kg * 42.3 m/s)
178.596 kg m/s = 86.6 kg * v + 2.538 kg m/s
175.058 kg m/s = 86.6 kg * v

To find v, we can divide both sides of the equation by 86.6 kg:
v = 175.058 kg m/s / 86.6 kg
v ≈ 2.019 m/s

Therefore, the velocity of the first person immediately after the snowball is thrown is approximately 2.019 m/s.