Recoil velocity on frictionless surface

[Valenti]

Homework Statement

A child stands on frictionless ice and throws a snowball. Estimate the recoil velocity of the child.

Homework Equations

m₁v_1i + m₂v_2i =m₁v₁ +m₂v_2f
1/2mv²_1i + 1/2 mv²_2i = 1/2 mv²_1f + 1/2mv²_2f

The Attempt at a Solution

After choosing estimates for weight of snowball, speed of child throwing snowball and weight of child I plugged it into the momentum and kinetic energy laws and solved for the final velocity in both of them, but I am not sure which equation is supposed to be used and in what situations

 

[gneill]

Show your work in detail.

 

[Valenti]

Show your work in detail.

Thanks, checked my work again and noticed i forgot to sq root for Vf in the KE formula, since it was negative only the momentum equation works. What type of questions would the KE formula be used though?

 

[gneill]

Kinetic energy is conserved when no external forces act on the system, or when there are no other avenues for energy loss or gain from the system. In perfectly elastic collisions kinetic energy is conserved. In inelastic collisions kinetic energy is not conserved.

A person throwing an object is equivalent to a "reverse" inelastic collision, where two bodies that were once connected are separated by some energy being injected: the person throwing the snowball is providing energy via their muscles, which is not accounted for by the simple conservation of KE formula applied to the individual masses.